International Journal of Scientific & Engineering Research, Volume 6, Issue 12, December ISSN
|
|
|
- Johnathan Griffith
- 6 years ago
- Views:
Transcription
1 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 0 ISSN -8 A Clss o New Bloc Geerlized Adms Implicit Ruge-Kutt Colloctio Metods Kumleg G.M., Collom J. P, Omgwu S. Abstrct I tis pper, te reormultio o te bloc geerlized Adms metods ito bloc geerlized Adms implicit Rug-Kutt metods or step umbers,,, is cosidered. Tis is becuse o te useuless o bloc implicit Ruge-Kutt metods or te solutio o sti ordir dieretil equtios. Te ew metods proposed i tis pper tur out to be A-stble d possess te stbilit properties o te Ruge-Kutt metods d ve implicit structure or ccurte d eiciet implemettio. Numericl exmples obtied demostrte te ccurc d eiciec o te ew bloc metods. Idex Terms A-stble, Geerlized Adms metods, Rug-Kutt metods d Sti Ordir Dieretil Equtios. Itroductio 0 ttp://
2 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 I erlier wor, Collom d Kumleg 0 costructed d implemeted clss o bloc Adms Moulto implicit Ruge KuttBmir metods or sti dieretil equtios. Te Bmir metods were sow to be A-stble d results obtied coverged to te exct solutio. Yubu 00, costructed oe-step bloc implicit Ruge Kutt colloctio metods or solvig sti ODEs, te scemes were obtied bsed o colloctio t Gussi poits d were sow to possess lrge regio o bsolute stbilit. Oter utors suc s Y d Adegboe 007, 0 ve costructed implicit bloc Ruge -Kutt metods bsed o te Qude s tpe or te solutio o sti ODEs. Te implicit Ruge-Kutt metods ve bee sow to be ver eective i te tretmet o sti iitil vlue problems s c be see i te wor o Axelso 6, Cipm 7. Te implicit Ruge-Kutt metods were ull developed bsed o te Gussi, Lobtto d Rduqudritures b Butcer d Wer 6. Gozlez-Pito et l 7 developed sigle Newto scemes or te solutio o te stge equtios o some implicit Ruge-utt metods suc s Guss, RduIIA d Lobtto IIIA wit our implicit stges. I tis pper, te reormultio o te bloc geerlized Adms metods s Bloc geerlized implicit Ruge- Kutt BGAIRK metods is cosidered or te solutio o iitil vlue problems o te orm ' x,, x 0 0, x [ b, ], R, be pproximtio to x, x,,,... d let 0 s te orm bii were i s i t ci, ij j, i,..., s j Te Butcer tbleu or te metod is give s c s c s c s s s ss b b x A implicit Ruge-Kutt metod s For te implicit Ruge Kutt metods, t ever step sstem o lgebric equtios wit s compoets s to be solved. Tis icreses te computtiol cost cosiderbl. Te New Metod b s Te costructio o bloc geerlized Adms metods or step umbers,, 0 ve bee cosidered i Kumleg 0usig te cotiuous iite dierece pproximtio d te iterpoltio d colloctio criteri described b Lie d Norsett 8 d Oumi et.l. Tese bloc metods were sow to ve good stbilit properties mig tem useul i te solutio o sti ODEs. To urter improve o te good stbilit properties o tese bloc metods, te reormultio o te metods ito bloc implicit Ruge- Kutt metods or step umbers,, is cosidered i tis pper. Te reormultio o te bloc geerlized Adms metodis cosidered ere becuse o te dvtges tt te implicit Ruge-Kutt metods ve over te covetiol lier multistep metods. Te bloc geerlized Adms metods cosidered b Kumleg 0 or step umbers,, re s ollows; Bloc geerlized Adms metod or step umber wit uiorm order 0 ttp://
3 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 0 ttp:// Bloc geerlized Adms metod or step umber wit uiorm order Bloc geerlized Adms metod or step umber wit uiorm order respectivel. Derivtio o BGAIRK Metod Te bloc GAMs re reormulted ito te BGAIRK Metod o order our b solvig tem simulteousl to rrive t 8 6 Its GAIRK metod wic is our stge implicit Ruge Kutt colloctio mil o uiorm order our is give s,,,, x x x x 7
4 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 Te crcteristic coeiciets o te BGAIRK metod re displed i orm o te Butcer tbleu s ollows: Derivtio o BGAIRK Metod Te bloc GAMs re lso reormulted ito te BGAIRK Metod o order ive b solvig tem simulteousl to rrive t Its GAIRK metod wic is ive stge implicit Ruge Kutt colloctio mil o uiorm order ive is give s x, x, x, x, x, Te crcteristic coeiciets o te BGAIRK metod re displed i orm o te Butcer tbleu s ollows: ttp://
5 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 Derivtio o BGAIRK Metod Te bloc GAMs re reormulted ito te BGAIRK Metod o order six b solvig tem simulteousl to rrive t Te GAIRK metod or 0 wic is six stge implicit Ruge Kutt colloctio mil o uiorm order six is give s x, x, x, x, x, 6 x, Te crcteristic coeiciets o te BGAIRK metod re displed i orm o te Butcer tbleu s ollows: ttp://
6 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 Absolute Stbilit Regios o te GAIRK Metods I tis sectio, te plots o te regio o bsolute stbilit o te ewl costructed GAIRK metods or s,, re cosidered. Tis is doe b reormultig te GAIRK metods s geerl lier metods itroduced b Burrge d Butcer, Butcer d Wer6 d urter cosidered b Collom 007. Te regios o bsolute stbilit o te GAIRK metods re s sow i ig.. Imz Imz Rez Rez Fig. Absolute Stbilit Regios o te Fig. Absolute Stbilit Regios o te GAIRK metod GAIRKmetod Imz Rez Fig. Absolute Stbilit Regios o te GAIRK metod Te regios i Fig d sows tt te GAIRK metods or d re A-stble sice teir regios o bsolute stbilit cotis te wole o te let-d l ple wile Fig revels tt te GAIRK metod or step umber is A-Stble. 0 ttp://
7 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 6 ISSN -8 Numericl Experimets I order to scerti te ccurc d eiciec o te GAIRK metods, umericl exmples re cosidered. Results obtied re compred wit LobttoIIIA metods o orders d 6 d te RduIIAmetod o order becuse o teir possessio o excellet stbilit d covergece properties or sti problems see Deer d Verwer 8, Butcer 87, Hirer d Wer 6.I ll te problems solved, 0. d0 x. Exmple. See Collom d Kumleg 0 ' 00si x, x si x0,0cos x 0.0e x Exmple. See Yubuet.l 0 ' 00 x x, 0, x x Exmple. e 00x - x - 000x - x ' , 0 0, x 000 e, 0, x e x e e Exmple ' x e Exmple gmr order LobttoIIIA order gmr order rdiia gmr order 6 LobttoIIIA order6 0.00E E E E E E00.0E-0.0E-0.8E-0.7E-0.E-0.E-0.7E-0.E-0.6E-0.68E-0.0E-0.E-0.7E-0.76E-0.E-0.0E-06.0E-0 8.8E-06.E-0 8.6E-0.07E-0.08E-08.E E E-06.E-0.E-06.8E E E-08.E E-06.8E-07.6E-08.E-08 8.E-0.E-07.E-06 6.E-08.E-08.E-08.E-0.8E E-07.0E-08.8E-08.E-0.E-0.7E-08.E-07.E-0.E-08.06E-0.6E-0.6E-08.E-07.07E-0.60E-08.8E-.0E-0 0 ttp://
8 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 7 ISSN -8 Exmple gmr order LobttoIIIA order gmr order rdiia order gmr order 6 LobttoIIIA order6 0.00E E E E E E00.0E-0.0E-0.8E-0.7E-0.E-0.E-0.7E-0.0E-0.6E-0.68E-0.0E-0.E-0.7E-0.E-0.E-0.8E-0.0E-0 8.8E-0.E-0.07E-0.07E-0 7.6E-06.E-0 8.E E-0.7E-0.E-0.70E E-0 8.E-06.8E-0.07E-0.8E-0.E-08.E E-07.E-0.0E-0 6.E-06.E-0.E-06 7.E-08.08E-0.7E-0.E-06.E-.E-07 7.E-0.E-06 7.E-0.0E-07.6E-.E E-0 6.E-07 8.E-0.7E-08.7E-.0E-0 6.7E- Exmple Gmr LobttoIIIA gmr Gmr LobttoIIIA order order rdiia order order 6 order6 0.00E E E E E E00.E E-0.E-0.E-0.E-0 7.8E-0.0E-0 7.7E-0.E-0 6.0E-0.E-0 6.8E-0.E-0 6.7E-0.E-0.76E-0 7.E-0.86E-0.0E-0.7E-0.E-0.77E-06.E-0.8E-0.8E-0.E-0 8.6E-0.E-06.8E-0.0E-0.6E-0.6E-0.0E-0.E-06.6E-0.7E-0.76E-0.06E-0.E-0.0E-06.7E-06.86E-0.E-0.6E-0.E-0.E-07.00E-06.6E-0.8E-0.E-0.E-06 8.E-07.0E-07.E-0.6E-0.7E-0.7E E E-07.06E-0 0 ttp://
9 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 8 ISSN -8 Exmple gmr order LobttoIIIA order gmr order rdiia gmr order 6 LobttoIIIA order6 0.00E E E E E E00.E-0.E-0 7.E-.08E-08.E-.E-0 8.7E-0 6.6E-0.7E-.00E-08.8E-.66E-.E-0 8.E-0.76E-.0E-0.7E-.0E-0 8.0E-0.00E-0.E- 8.E-0.E-.E- 7.E-0.E-0.8E- 7.E-0.0E- 7.E- 6.67E-0.E-0.6E- 6.7E-0.E-.E- 6.06E-0.7E-0.E- 6.0E-0.E-.68E-.8E-0.0E-0.8E-.E-0.6E-.E-.6E-0.E-0.6E-.E-0.7E-.E-.8E-0.0E-0.E-.E-0.E-.E- Coclusio Te umericl results rom Tbles to revel te ccurc o te ewl costructed clss o bloc Geerlized Adms implicit Ruge Kutt metods or step umbers, d. It c be see clerl rom Tble, d tt our ew metods perorm better t te Lobtto IIIA metod o order, Lobtto IIIA o order 6 d te Rdu IIA metod o order or te problems solved i exmples, d. However, or exmple, Tble revels tt our ew metods compete well wit te Rdu IIA metod o order. It ws lso observed tt te ew metods ve better stbilit regios t te covetiol bloc geerlized Adms metods. Reereces [] O.Axelso, A Clss o A-Stble Metods. BIT,,8-6. [] J.C.Buctcer, Te Numericl Alsis o Ordir Dieretil Equtios, Jo Wile d Sos, Cicester 87.. [] J. C.Buctcer, G.Wer, Ruge Kutt metods: Some Historicl otes, Jourl o Applied Numericl Mtemtics, - 6. [] K. Burrge,J.C. Butcer, No Lier Stbilit or Geerl Clss o Dieretil Equtios Metod. BIT 0, 8-0. [] F.H.Cipm, A-stble Ruge-Kutt Processes. BIT,, [6] J.P. Collom, G.M. Kumleg, A Clss o Bloc Hbrid Adms Moulto Implicit Ruge-Kutt Bmir Metods or Sti Ordir Dieretil Equtios. Itertiol Jourl o Mtemtics d Computtios [7] K. Deer d J. G. Verwer, Stbilit o Ruge Kutt metods or Sti Nolier Dieretil Equtios. Nort-Holld, Amsterdm.8 [8] J.P.Collom, J.N. Ndm d G.M.Kumleg, O Some Properties o te Bloc Lier Multistep Metods. Sciece World Jourl,, [] S.Gozlez-Pito, S. perez-rodriquez, J.I. Motijo, O te umericl solutio o sti IVP s b Lobtto IIIA ruge-utt metod. Jourl o Computtiol d Applied Mtemtics, 8,-8 7. [0] E. Hirer, d G. Wer, Solvig Ordir Dieretil Equtios II, Spriger-Verlg, Berli 6. [] G.M. Kumleg, Cotiuous Geerlized Adms Metods i Bloc Form or Te Solutio o Nolier Ordir Dieretil Equtios. PD Tesis Upublised Uiversit o Jos ttp://
10 Itertiol Jourl o Scietiic & Egieerig Reserc, Volume 6, Issue, December-0 ISSN -8 [] I Lie d S. P. Norsett, Super covergece or Multistep Colloctio. Mtemtics o Computtio. 8, [] P. Oumi, D.O. Awoemi, S.N. Jtor d U.W. Sirise, New Lier Multistep Metods wit Cotiuous Coeiciets or First Order Iitil Vlue Problems. Jourl o te Nigeri Mtemticl Societ., 7. [] D.G. Yubu, New Bloc Implicit Ruge-Kutt Colloctio Metods or Solvig Sti Dieretil Equtios. Abcus A [] D.G. Yubu, N.H. Mj, S.S. Bub, A.I. Ms, A Fmil o Uiorml Accurte Order Lobtto-Ruge-Kutt Colloctio Metods. Comput. Appl. Mt Geore Mic Kumleg s obtied PD degree i Numericl lsis. Presetl He lectures mtemtics course i te Uiversit o Jos, Jos Nigeri, PH E-mil: umleg_g@oo.com Josu Pm Collom s obtied PD degree i Numericl lsis. Presetl He is ssocite Proessor o mtemtics i umericl lsis i te Uiversit o Jos, Jos Nigeri, PH-070. E-mil: collomjp@oo.com Smso Omgwu is curretl pursuig PD degree progrm i mtemtics umericl lsis i Uiversit o Jos, Jos Nigeri, PH E-mil: smsoomgwu@oo.com 0 ttp://
A 4-Step Implicit Collocation Method for Solution of First and Second Order Odes
Itertiol Jourl o Sciece d Tecolog Volume No. November A -Step Implicit Colloctio Metod or Solutio o First d Secod Order Odes Z A. Adegboe I. Aliu Deprtmet o Mts/Stts/Computer Sciece Kdu Poltecic Kdu.Nigeri.
1. Introduction. 2. Numerical Methods
America Joural o Computatioal ad Applied Matematics, (5: 9- DOI:.59/j.ajcam.5. A Stud o Numerical Solutios o Secod Order Iitial Value Problems (IVP or Ordiar Dieretial Equatios wit Fourt Order ad Butcer
Comparison of B-spline Method and Finite Difference Method to Solve BVP of Linear ODEs
JOURNAL OF COMPUTERS VOL. 6 NO. OCTOER Compriso of -splie Metod d Fiite Differece Metod to Solve VP of Lier ODEs Jici Cg Qili Yg Log Zo College of ScieceHebei Uited Uiversit Tgs Hebei 6Ci {ici@eut.edu.c}
Some New Iterative Methods Based on Composite Trapezoidal Rule for Solving Nonlinear Equations
Itertiol Jourl of Mthemtics d Sttistics Ivetio (IJMSI) E-ISSN: 31 767 P-ISSN: 31-759 Volume Issue 8 August. 01 PP-01-06 Some New Itertive Methods Bsed o Composite Trpezoidl Rule for Solvig Nolier Equtios
A Class of Blended Block Second Derivative Multistep Methods for Stiff Systems
Iteratioal Joural of Iovative Mathematics, Statistics & Eerg Policies ():-6, Ja.-Mar. 7 SEAHI PUBLICATIONS, 7 www.seahipa.org ISSN: 67-8X A Class of Bleded Bloc Secod Derivative Multistep Methods for Stiff
NUMERICAL DIFFERENTIAL 1
NUMERICAL DIFFERENTIAL Ruge-Kutta Metods Ruge-Kutta metods are ver popular ecause o teir good eiciec; ad are used i most computer programs or dieretial equatios. Te are sigle-step metods as te Euler metods.
An Improved Self-Starting Implicit Hybrid Method
IOSR Joural o Matematics (IOSR-JM e-issn: 78-78, p-issn:9-76x. Volume 0, Issue Ver. II (Mar-Apr. 04, PP 8-6 www.iosrourals.org A Improved Sel-Startig Implicit Hbrid Metod E. O. Adeea Departmet o Matematics/Statistics,
Angle of incidence estimation for converted-waves
Agle of icidece estimtio for coverted-wves Crlos E. Nieto d Robert R. tewrt Agle of icidece estimtio ABTRACT Amplitude-versus-gle AA lysis represets li betwee te geologicl properties of roc iterfces d
Variational Iteration Method for Solving Volterra and Fredholm Integral Equations of the Second Kind
Ge. Mth. Notes, Vol. 2, No. 1, Jury 211, pp. 143-148 ISSN 2219-7184; Copyright ICSRS Publictio, 211 www.i-csrs.org Avilble free olie t http://www.gem.i Vritiol Itertio Method for Solvig Volterr d Fredholm
Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials
Numericl Solutios of Fredholm Itegrl Equtios Usig erstei Polyomils A. Shiri, M. S. Islm Istitute of Nturl Scieces, Uited Itertiol Uiversity, Dhk-, gldesh Deprtmet of Mthemtics, Uiversity of Dhk, Dhk-,
Power Series Solutions to Generalized Abel Integral Equations
Itertiol Jourl of Mthemtics d Computtiol Sciece Vol., No. 5, 5, pp. 5-54 http://www.isciece.org/jourl/ijmcs Power Series Solutios to Geerlized Abel Itegrl Equtios Rufi Abdulli * Deprtmet of Physics d Mthemtics,
Integral Operator Defined by k th Hadamard Product
ITB Sci Vol 4 A No 35-5 35 Itegrl Opertor Deied by th Hdmrd Product Msli Drus & Rbh W Ibrhim School o Mthemticl Scieces Fculty o sciece d Techology Uiversiti Kebgs Mlysi Bgi 436 Selgor Drul Ehs Mlysi Emil:
lecture 16: Introduction to Least Squares Approximation
97 lecture 16: Itroductio to Lest Squres Approximtio.4 Lest squres pproximtio The miimx criterio is ituitive objective for pproximtig fuctio. However, i my cses it is more ppelig (for both computtio d
SOLUTION OF DIFFERENTIAL EQUATION FOR THE EULER-BERNOULLI BEAM
Jourl of Applied Mthemtics d Computtiol Mechics () 57-6 SOUION O DIERENIA EQUAION OR HE EUER-ERNOUI EAM Izbel Zmorsk Istitute of Mthemtics Czestochow Uiversit of echolog Częstochow Pold izbel.zmorsk@im.pcz.pl
Numerical Integration - (4.3)
Numericl Itegrtio - (.). Te Degree of Accurcy of Qudrture Formul: Te degree of ccurcy of qudrture formul Qf is te lrgest positive iteger suc tt x k dx Qx k, k,,,...,. Exmple fxdx 9 f f,,. Fid te degree
A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation
Joural of Matematics ad Statistics 4 (: 7-, 008 ISSN 549-3644 008 Sciece Publicatios A Pseudo Splie Metods for Solvig a Iitial Value Problem of Ordiary Differetial Equatio B.S. Ogudare ad G.E. Okeca Departmet
Schrödinger Equation Via Laplace-Beltrami Operator
IOSR Jourl of Mthemtics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume 3, Issue 6 Ver. III (Nov. - Dec. 7), PP 9-95 www.iosrjourls.org Schrödiger Equtio Vi Lplce-Beltrmi Opertor Esi İ Eskitşçioğlu,
Closed Newton-Cotes Integration
Closed Newto-Cotes Itegrtio Jmes Keeslig This documet will discuss Newto-Cotes Itegrtio. Other methods of umericl itegrtio will be discussed i other posts. The other methods will iclude the Trpezoidl Rule,
MAT641- Numerical Analysis (Master course) D. Samy MZIOU
Syllbus: MAT64- Numericl Alysis Mster course - - - D. Smy MZIOU Review: Clculus lier Algebr Numericl Alysis MATLAB sotwre will be used itesively i this course There will be regulr homewor ssigmets, usully
Autar Kaw Benjamin Rigsby. Transforming Numerical Methods Education for STEM Undergraduates
Autr Kw Bejmi Rigsby http://m.mthforcollege.com Trsformig Numericl Methods Eductio for STEM Udergrdutes http://m.mthforcollege.com . solve set of simulteous lier equtios usig Nïve Guss elimitio,. ler the
Attempt any TEN of the following:
(ISO/IEC - 7-5 Certiied) Importt Istructios to emiers: ) Te swers sould be emied b ke words d ot s word-to-word s gie i te model swer sceme. ) Te model swer d te swer writte b cdidte m r but te emier m
A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation
Joural of Matematics Researc; Vol No ; ISSN - E-ISSN - Publised b Caadia Ceter of Sciece ad Educatio A New Hbrid i te Noliear Part of Adomia Decompositio Metod for Iitial Value Problem of Ordiar Differetial
0 otherwise. sin( nx)sin( kx) 0 otherwise. cos( nx) sin( kx) dx 0 for all integers n, k.
. Computtio of Fourier Series I this sectio, we compute the Fourier coefficiets, f ( x) cos( x) b si( x) d b, i the Fourier series To do this, we eed the followig result o the orthogolity of the trigoometric
SOLUTION OF SYSTEM OF LINEAR EQUATIONS. Lecture 4: (a) Jacobi's method. method (general). (b) Gauss Seidel method.
SOLUTION OF SYSTEM OF LINEAR EQUATIONS Lecture 4: () Jcobi's method. method (geerl). (b) Guss Seidel method. Jcobi s Method: Crl Gustv Jcob Jcobi (804-85) gve idirect method for fidig the solutio of system
Numerical Derivatives by Symbolic Tools in MATLAB
Numerical Derivatives by Symbolic ools i MALAB Mig-Gog Lee * ad Rei-Wei Sog ad Hsuag-Ci Cag mglee@cu.edu.tw * Departmet o Applied Matematics Cug Hua Uiversity Hsicu, aiwa Abstract: Numerical approaces
Numerical Solution of Fuzzy Fredholm Integral Equations of the Second Kind using Bernstein Polynomials
Jourl of Al-Nhri Uiversity Vol.5 (), Mrch,, pp.-9 Sciece Numericl Solutio of Fuzzy Fredholm Itegrl Equtios of the Secod Kid usig Berstei Polyomils Srmd A. Altie Deprtmet of Computer Egieerig d Iformtio
A general theory of minimal increments for Hirsch-type indices and applications to the mathematical characterization of Kosmulski-indices
Mlysi Jourl of Librry & Iformtio Sciece, Vol. 9, o. 3, 04: 4-49 A geerl theory of miiml icremets for Hirsch-type idices d pplictios to the mthemticl chrcteriztio of Kosmulski-idices L. Egghe Uiversiteit
THE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK SUMMER EXAMINATION 2005 FIRST ENGINEERING
OLLSCOIL NA héireann, CORCAIGH THE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK SUMMER EXAMINATION 2005 FIRST ENGINEERING MATHEMATICS MA008 Clculus d Lier
A NUMERICAL METHOD OF SOLVING CAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONS BASED ON A LINEAR APPROXIMATION
U.P.B. Sci. Bull., Series A, Vol. 79, Iss. 4, 7 ISSN -77 A NUMERICAL METHOD OF SOLVING CAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONS BASED ON A LINEAR APPROXIMATION Cristia ŞERBĂNESCU, Marius BREBENEL A alterate
Fast Fourier Transform 1) Legendre s Interpolation 2) Vandermonde Matrix 3) Roots of Unity 4) Polynomial Evaluation
Algorithm Desig d Alsis Victor Admchi CS 5-45 Sprig 4 Lecture 3 J 7, 4 Cregie Mello Uiversit Outlie Fst Fourier Trsform ) Legedre s Iterpoltio ) Vdermode Mtri 3) Roots of Uit 4) Polomil Evlutio Guss (777
Modified chain least squares method and some numerical results
IJST (2015) 39A1: 91-99 Iri Jourl of Sciece & Tecology ttp://ijsts.sirzu.c.ir Modified ci lest squres metod d some umericl results F. Goree 1, E. Boli 1 * d A. Adolli 2 1 Deprtmet of Mtemtics, College
We will begin by supplying the proof to (a).
(The solutios of problem re mostly from Jeffrey Mudrock s HWs) Problem 1. There re three sttemet from Exmple 5.4 i the textbook for which we will supply proofs. The sttemets re the followig: () The spce
Digital Signal Processing, Fall 2006
Digitl Sigl Processig, Fll 6 Lecture 6: Sstem structures for implemettio Zeg-u T Deprtmet of Electroic Sstems Alorg Uiversit, Demr t@om.u.d Digitl Sigl Processig, VI, Zeg-u T, 6 Course t glce Discrete-time
THE SOLUTION OF THE FRACTIONAL DIFFERENTIAL EQUATION WITH THE GENERALIZED TAYLOR COLLOCATIN METHOD
IJRRAS August THE SOLUTIO OF THE FRACTIOAL DIFFERETIAL EQUATIO WITH THE GEERALIZED TAYLOR COLLOCATI METHOD Slih Ylçıbş Ali Kourlp D. Dömez Demir 3* H. Hilmi Soru 4 34 Cell Byr Uiversity Fculty of Art &
Remarks: (a) The Dirac delta is the function zero on the domain R {0}.
Sectio Objective(s): The Dirc s Delt. Mi Properties. Applictios. The Impulse Respose Fuctio. 4.4.. The Dirc Delt. 4.4. Geerlized Sources Defiitio 4.4.. The Dirc delt geerlized fuctio is the limit δ(t)
More Elementary Aspects of Numerical Solutions of PDEs!
ttp://www.d.edu/~gtryggva/cfd-course/ Outlie More Elemetary Aspects o Numerical Solutios o PDEs I tis lecture we cotiue to examie te elemetary aspects o umerical solutios o partial dieretial equatios.
Topic 6b Finite Difference Approximations
/8/8 Course Instructor Dr. Rymond C. Rump Oice: A 7 Pone: (95) 747 6958 E Mil: rcrump@utep.edu Topic 6b Finite Dierence Approximtions EE 486/5 Computtionl Metods in EE Outline Wt re inite dierence pproximtions?
Solving third order boundary value problem with fifth order block method
Matematical Metods i Egieerig ad Ecoomics Solvig tird order boudary value problem wit it order bloc metod A. S. Abdulla, Z. A. Majid, ad N. Seu Abstract We develop a it order two poit bloc metod or te
Key words. Numerical quadrature, piecewise polynomial, convergence rate, trapezoidal rule, midpoint rule, Simpson s rule, spectral accuracy.
O SPECTRA ACCURACY OF QUADRATURE FORMUAE BASED O PIECEWISE POYOMIA ITERPOATIO A KURGAOV AD S TSYKOV Abstrct It is well-known tt te trpezoidl rule, wile being only second-order ccurte in generl, improves
Chapter 25 Sturm-Liouville problem (II)
Chpter 5 Sturm-Liouville problem (II Speer: Lug-Sheg Chie Reerece: [] Veerle Ledou, Study o Specil Algorithms or solvig Sturm-Liouville d Schrodiger Equtios. [] 王信華教授, chpter 8, lecture ote o Ordiry Dieretil
Convergence rates of approximate sums of Riemann integrals
Jourl of Approximtio Theory 6 (9 477 49 www.elsevier.com/locte/jt Covergece rtes of pproximte sums of Riem itegrls Hiroyuki Tski Grdute School of Pure d Applied Sciece, Uiversity of Tsukub, Tsukub Ibrki
On Exact Finite-Difference Scheme for Numerical Solution of Initial Value Problems in Ordinary Differential Equations.
O Exact Fiite-Differece Sceme for Numerical Solutio of Iitial Value Problems i Ordiar Differetial Equatios. Josua Suda, M.Sc. Departmet of Matematical Scieces, Adamawa State Uiversit, Mubi, Nigeria. E-mail:
Interpolation. 1. What is interpolation?
Iterpoltio. Wht is iterpoltio? A uctio is ote give ol t discrete poits such s:.... How does oe id the vlue o t other vlue o? Well cotiuous uctio m e used to represet the + dt vlues with pssig through the
Stability analysis of numerical methods for stochastic systems with additive noise
Stability aalysis of umerical metods for stoctic systems wit additive oise Yosiiro SAITO Abstract Stoctic differetial equatios (SDEs) represet pysical peomea domiated by stoctic processes As for determiistic
UNISA NUMERICAL METHODS (COS 233-8) Solutions to October 2000 Final Exams
UNISA NUMERICAL METHODS COS -8 Solutios to October Fil Ems Questio Re: Tble 4. pge 47 o Gerld/Wetley [ d editio] Write dow te itertio scemes or i ii iii te bisectio metod; te metod o lse positio regul
Numerical method for solving system of Fredhlom integral equations using Chebyshev cardinal functions
2014 2014) 1-13 Avilble olie t www.ispcs.com/cte Volume 2014, Yer 2014 Article ID cte-00165, 13 Pges doi:10.5899/2014/cte-00165 Reserch Article umericl method for solvig system of Fredhlom itegrl equtios
A GENERAL METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS: THE FROBENIUS (OR SERIES) METHOD
Diol Bgoo () A GENERAL METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS: THE FROBENIUS (OR SERIES) METHOD I. Itroductio The first seprtio of vribles (see pplictios to Newto s equtios) is ver useful method
Trapezoidal Rule of Integration
Trpezoidl Rule o Itegrtio Civil Egieerig Mjors Authors: Autr Kw, Chrlie Brker http://umericlmethods.eg.us.edu Trsormig Numericl Methods Eductio or STEM Udergrdutes /0/00 http://umericlmethods.eg.us.edu
x x x 2x x N ( ) p NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS By Newton-Raphson formula
NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS. If g( is cotiuous i [a,b], te uder wat coditio te iterative (or iteratio metod = g( as a uique solutio i [a,b]? '( i [a,b].. Wat
Some Properties of Brzozowski Derivatives of Regular Expressions
Itertiol Jourl of Computer Treds d Techology (IJCTT) volume 13 umber 1 Jul 014 Some Properties of Brzozoski erivtives of Regulr Expressios NMuruges #1, OVShmug Sudrm * #1 Assistt Professor, ept of Mthemtics,
1. (25 points) Use the limit definition of the definite integral and the sum formulas to compute. [1 x + x2
Mth 3, Clculus II Fil Exm Solutios. (5 poits) Use the limit defiitio of the defiite itegrl d the sum formuls to compute 3 x + x. Check your swer by usig the Fudmetl Theorem of Clculus. Solutio: The limit
Orthogonal functions - Function Approximation
Orthogol uctios - Fuctio Approimtio - he Problem - Fourier Series - Chebyshev Polyomils he Problem we re tryig to pproimte uctio by other uctio g which cosists o sum over orthogol uctios Φ weighted by
Math Week 5 concepts and homework, due Friday February 10
Mt 2280-00 Week 5 concepts nd omework, due Fridy Februry 0 Recll tt ll problems re good for seeing if you cn work wit te underlying concepts; tt te underlined problems re to be nded in; nd tt te Fridy
On the convergence, consistence and stability of a standard finite difference scheme
AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 2, Sciece Huβ, ttp://www.sciub.org/ajsir ISSN: 253-649X, doi:.525/ajsir.2.2.2.74.78 O te covergece, cosistece ad stabilit of a stadard fiite differece
Pre-Calculus - Chapter 3 Sections Notes
Pre-Clculus - Chpter 3 Sectios 3.1-3.4- Notes Properties o Epoets (Review) 1. ( )( ) = + 2. ( ) =, (c) = 3. 0 = 1 4. - = 1/( ) 5. 6. c Epoetil Fuctios (Sectio 3.1) Deiitio o Epoetil Fuctios The uctio deied
A New Estimator Using Auxiliary Information in Stratified Adaptive Cluster Sampling
Ope Jourl of ttitic, 03, 3, 78-8 ttp://d.doi.org/0.436/oj.03.3403 Publied Olie eptember 03 (ttp://www.cirp.org/jourl/oj) New Etimtor Uig uilir Iformtio i trtified dptive Cluter mplig Nippor Cutim *, Moc
CONVERGENCE OF THE RATIO OF PERIMETER OF A REGULAR POLYGON TO THE LENGTH OF ITS LONGEST DIAGONAL AS THE NUMBER OF SIDES OF POLYGON APPROACHES TO
CONVERGENCE OF THE RATIO OF PERIMETER OF A REGULAR POLYGON TO THE LENGTH OF ITS LONGEST DIAGONAL AS THE NUMBER OF SIDES OF POLYGON APPROACHES TO Pw Kumr BK Kthmdu, Nepl Correspodig to: Pw Kumr BK, emil:
Fourier Series and Applications
9/7/9 Fourier Series d Applictios Fuctios epsio is doe to uderstd the better i powers o etc. My iportt probles ivolvig prtil dieretil equtios c be solved provided give uctio c be epressed s iiite su o
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Assoc. Prof. Dr. Bur Kelleci Sprig 8 OUTLINE The Z-Trsform The Regio of covergece for the Z-trsform The Iverse Z-Trsform Geometric
Certain sufficient conditions on N, p n, q n k summability of orthogonal series
Avilble olie t www.tjs.com J. Nolier Sci. Appl. 7 014, 7 77 Reserch Article Certi sufficiet coditios o N, p, k summbility of orthogol series Xhevt Z. Krsiqi Deprtmet of Mthemtics d Iformtics, Fculty of
On One Justification on the Use of Hybrids for the Solution of First Order Initial Value Problems of Ordinary Differential Equations
Pure and Applied Matematics Journal 7; 6(5: 74 ttp://wwwsciencepublisinggroupcom/j/pamj doi: 648/jpamj765 ISSN: 6979 (Print; ISSN: 698 (Online On One Justiication on te Use o Hybrids or te Solution o First
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 0 FURTHER CALCULUS II. Sequeces d series. Rolle s theorem d me vlue theorems 3. Tlor s d Mcluri s theorems 4. L Hopitl
Numerical Integration by using Straight Line Interpolation Formula
Glol Jourl of Pure d Applied Mthemtics. ISSN 0973-1768 Volume 13, Numer 6 (2017), pp. 2123-2132 Reserch Idi Pulictios http://www.ripulictio.com Numericl Itegrtio y usig Stright Lie Iterpoltio Formul Mhesh
Module 4. Signal Representation and Baseband Processing. Version 2 ECE IIT, Kharagpur
Module 4 Sigl Represettio d Bsed Processig Versio ECE IIT, Khrgpur Lesso 5 Orthogolity Versio ECE IIT, Khrgpur Ater redig this lesso, you will ler out Bsic cocept o orthogolity d orthoormlity; Strum -
Trapezoidal Rule of Integration
Trpezoidl Rule o Itegrtio Mjor: All Egieerig Mjors Authors: Autr Kw, Chrlie Brker Trsormig Numericl Methods Eductio or STEM Udergrdutes /0/200 Trpezoidl Rule o Itegrtio Wht is Itegrtio Itegrtio: The process
2. General formula for Runge-Kutta methods
NOLTA, IEICE Pper Equivlent circuits for implicit unge-kutt metods in circuit simultors for nonliner circuits Ysuiko Toym 1), Ttusy Kuwzki 1, nd Jun Sirtki 1 Mkiko Okumur 1 1 Kngw Institute of Tecnology,
Quadrature Methods for Numerical Integration
Qudrture Methods for Numericl Itegrtio Toy Sd Istitute for Cle d Secure Eergy Uiversity of Uth April 11, 2011 1 The Need for Numericl Itegrtio Nuemricl itegrtio ims t pproximtig defiite itegrls usig umericl
( ) k ( ) 1 T n 1 x = xk. Geometric series obtained directly from the definition. = 1 1 x. See also Scalars 9.1 ADV-1: lim n.
Sclrs-9.0-ADV- Algebric Tricks d Where Tylor Polyomils Come From 207.04.07 A.docx Pge of Algebric tricks ivolvig x. You c use lgebric tricks to simplify workig with the Tylor polyomils of certi fuctios..
Isolating the Polynomial Roots with all Zeros Real
th WSEAS Itertiol Coferece o COMPUTERS Herlio Greece July 3-5 008 Isoltig the Polyomil Roots with ll Zeros Rel MURESAN ALEXE CALIN Deprtmet of Mthemtics Uiversity Petroleum d Gs Ploiesti Romi Str Democrtiei
Definite Integral. The Left and Right Sums
Clculus Li Vs Defiite Itegrl. The Left d Right Sums The defiite itegrl rises from the questio of fidig the re betwee give curve d x-xis o itervl. The re uder curve c be esily clculted if the curve is give
INFINITE SERIES. ,... having infinite number of terms is called infinite sequence and its indicated sum, i.e., a 1
Appedix A.. Itroductio As discussed i the Chpter 9 o Sequeces d Series, sequece,,...,,... hvig ifiite umber of terms is clled ifiite sequece d its idicted sum, i.e., + + +... + +... is clled ifite series
The evaluation of P, and T from these formulae indeed requires that the energy E be expressed as a function of the quantities N, V and S.
d dq, dq d d d, d d d d, e evlutio of, d from tese formule ideed requires tt te eerg be epressed s fuctio of te qutities, d. f (,,) is sould, i priciple, be possible oce is kow s fuctio of, d. f (,, )
=> PARALLEL INTERCONNECTION. Basic Properties LTI Systems. The Commutative Property. Convolution. The Commutative Property. The Distributive Property
Lier Time-Ivrit Bsic Properties LTI The Commuttive Property The Distributive Property The Associtive Property Ti -6.4 / Chpter Covolutio y ] x ] ] x ]* ] x ] ] y] y ( t ) + x( τ ) h( t τ ) dτ x( t) * h(
Vectors. Vectors in Plane ( 2
Vectors Vectors i Ple ( ) The ide bout vector is to represet directiol force Tht mes tht every vector should hve two compoets directio (directiol slope) d mgitude (the legth) I the ple we preset vector
Appendix A Examples for Labs 1, 2, 3 1. FACTORING POLYNOMIALS
Appedi A Emples for Ls,,. FACTORING POLYNOMIALS Tere re m stdrd metods of fctorig tt ou ve lered i previous courses. You will uild o tese fctorig metods i our preclculus course to ele ou to fctor epressios
The Reimann Integral is a formal limit definition of a definite integral
MATH 136 The Reim Itegrl The Reim Itegrl is forml limit defiitio of defiite itegrl cotiuous fuctio f. The costructio is s follows: f ( x) dx for Reim Itegrl: Prtitio [, ] ito suitervls ech hvig the equl
Reduction of Higher Order Linear Ordinary Differential Equations into the Second Order and Integral Evaluation of Exact Solutions
Mthemtic Aeter, Vol. 4, 04, o., 75-89 Reductio o Higher Order Lier Ordiry Dieretil Equtios ito the Secod Order d Itegrl Evlutio o Ect Solutios Guw Nugroho* Deprtmet o Egieerig Physics, Istitut Tekologi
Green s Function Approach to Solve a Nonlinear Second Order Four Point Directional Boundary Value Problem
IOSR Jourl of Mthemtics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume 3, Issue 3 Ver. IV (My - Jue 7), PP -8 www.iosrjourls.org Gree s Fuctio Approch to Solve Nolier Secod Order Four Poit Directiol
Solution of the exam in TMA4212 Monday 23rd May 2013 Time: 9:00 13:00
Norwegi Uiversity of Sciece d Techology Deprtmet of Mthemticl Scieces Cotct durig the exm: Ele Celledoi, tlf. 735 93541 Pge 1 of 7 of the exm i TMA4212 Mody 23rd My 2013 Time: 9:00 13:00 Allowed ids: Approved
Famurewa O. K. E*, Ademiluyi R. A. and Awoyemi D. O.
Africa Joural of Matematics ad omputer Sciece Researc Vol. (), pp. -, Marc Available olie at ttp://www.academicourals.org/ajmsr ISSN 6-97 Academic Jourals Full Legt Researc Paper A comparative stud of
On the Derivation and Implementation of a Four Stage Harmonic Explicit Runge-Kutta Method *
Applied Mathematics, 05, 6, 694-699 Published Olie April 05 i SciRes. http://www.scirp.org/joural/am http://dx.doi.org/0.46/am.05.64064 O the Derivatio ad Implemetatio of a Four Stage Harmoic Explicit
SOME SHARP OSTROWSKI-GRÜSS TYPE INEQUALITIES
Uiv. Beogrd. Publ. Elektroteh. Fk. Ser. Mt. 8 006 4. Avilble electroiclly t http: //pefmth.etf.bg.c.yu SOME SHARP OSTROWSKI-GRÜSS TYPE INEQUALITIES Zheg Liu Usig vrit of Grüss iequlity to give ew proof
Here and further the following reduction of record is applied.
MODL OF SRSSD-SRAIND SA OF MULILAYR MASSS WIH RGARD FOR NON-IDAL CONAC OF LAYRS V.G.Piskuov, A.V.Mrchuk We cosider lyered desig i rectgulr crtesi system o coordites. o xes o coordites x, y, there corresod
Convergence of the FEM. by Hui Zhang Jorida Kushova Ruwen Jung
Covergece o te FEM by Hi Zg Jorid Ksov Rwe Jg I order to proo FEM soltios to be coverget, mesremet or teir qlity is reqired. A simple pproc i ect soltio is ccessible is to qtiy te error betwee FEMd te
Modification of Weerakoon-Fernando s Method with Fourth-Order of Convergence for Solving Nonlinear Equation
ISSN: 50-08 Iteratioal Joural o AdvacedResearch i Sciece, Egieerig ad Techology Vol. 5, Issue 8, August 018 Modiicatio o Weerakoo-Ferado s Method with Fourth-Order o Covergece or Solvig Noliear Equatio
2.1.1 Definition The Z-transform of a sequence x [n] is simply defined as (2.1) X re x k re x k r
![2.1.1 Definition The Z-transform of a sequence x [n] is simply defined as (2.1) X re x k re x k r](/thumbs/82/85448174.jpg "2.1.1 Definition The Z-transform of a sequence x [n] is simply defined as (2.1) X re x k re x k r")
Z-Trsforms. INTRODUCTION TO Z-TRANSFORM The Z-trsform is coveiet d vluble tool for represetig, lyig d desigig discrete-time sigls d systems. It plys similr role i discrete-time systems to tht which Lplce
SUTCLIFFE S NOTES: CALCULUS 2 SWOKOWSKI S CHAPTER 11
SUTCLIFFE S NOTES: CALCULUS SWOKOWSKI S CHAPTER Ifiite Series.5 Altertig Series d Absolute Covergece Next, let us cosider series with both positive d egtive terms. The simplest d most useful is ltertig
CS537. Numerical Analysis and Computing
CS57 Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 Jauary 9 9 What is the Root May physical system ca be
Approximations of Definite Integrals
Approximtios of Defiite Itegrls So fr we hve relied o tiderivtives to evlute res uder curves, work doe by vrible force, volumes of revolutio, etc. More precisely, wheever we hve hd to evlute defiite itegrl
Week 13 Notes: 1) Riemann Sum. Aim: Compute Area Under a Graph. Suppose we want to find out the area of a graph, like the one on the right:
Week 1 Notes: 1) Riem Sum Aim: Compute Are Uder Grph Suppose we wt to fid out the re of grph, like the oe o the right: We wt to kow the re of the red re. Here re some wys to pproximte the re: We cut the
The Weierstrass Approximation Theorem
The Weierstrss Approximtio Theorem Jmes K. Peterso Deprtmet of Biologicl Scieces d Deprtmet of Mthemticl Scieces Clemso Uiversity Februry 26, 2018 Outlie The Wierstrss Approximtio Theorem MtLb Implemettio
Lecture 4 Recursive Algorithm Analysis. Merge Sort Solving Recurrences The Master Theorem
Lecture 4 Recursive Algorithm Alysis Merge Sort Solvig Recurreces The Mster Theorem Merge Sort MergeSortA, left, right) { if left < right) { mid = floorleft + right) / 2); MergeSortA, left, mid); MergeSortA,
Image Motion Analysis
Deprtmet o Computer Egieerig Uiersit o Cliori t St Cru Imge Motio Alsis CME 64: Imge Alsis Computer Visio Hi o Imge sequece motio Deprtmet o Computer Egieerig Uiersit o Cliori t St Cru Imge sequece processig
CHAPTER 6c. NUMERICAL INTERPOLATION
CHAPTER 6c. NUMERICAL INTERPOLATION A. J. Clark School o Egieerig Departmet o Civil ad Evirometal Egieerig y Dr. Irahim A. Assakka Sprig ENCE - Computatio Methods i Civil Egieerig II Departmet o Civil
Some Variants of Newton's Method with Fifth-Order and Fourth-Order Convergence for Solving Nonlinear Equations
Copyright, Darbose Iteratioal Joural o Applied Mathematics ad Computatio Volume (), pp -6, 9 http//: ijamc.darbose.com Some Variats o Newto's Method with Fith-Order ad Fourth-Order Covergece or Solvig
The limit comparison test
Roerto s Notes o Ifiite Series Chpter : Covergece tests Sectio 4 The limit compriso test Wht you eed to kow lredy: Bsics of series d direct compriso test. Wht you c ler here: Aother compriso test tht does
Toeplitz and Translation Operators on the q-fock Spaces *
Advces i Pure Mthemtics 35-333 doi:436/pm659 Published Olie November (http://wwwscirporg/jourl/pm) Toeplit d Trsltio Opertors o the -Foc Spces * Abstrct Fethi Solti Higher College o Techology d Iormtics
A Self-Starting Hybrid Linear Multistep Method for a Direct Solution of the General Second-Order Initial Value Problem
IOS Joural o Matematics (IOS-JM) ISSN: 78-578. Volume 4 Issue 6 (Ja. - eb. ) PP 7- www.iosrourals.org Sel-Startig Hbrid Liear Multistep Metod or a Direct Solutio o te Geeral Secod-Order Iitial Value Problem
Chapter 7 Infinite Series
MA Ifiite Series Asst.Prof.Dr.Supree Liswdi Chpter 7 Ifiite Series Sectio 7. Sequece A sequece c be thought of s list of umbers writte i defiite order:,,...,,... 2 The umber is clled the first term, 2
Thomas J. Osler Mathematics Department Rowan University Glassboro NJ Introduction
Ot 0 006 Euler s little summtio formul d speil vlues of te zet futio Toms J Osler temtis Deprtmet Row Uiversity Glssboro J 0608 Osler@rowedu Itrodutio I tis ote we preset elemetry metod of determiig vlues