Modified Decomposition Method for Solution of Fractional Partial Differential Equations of Two-Sided
|
|
|
- Rebecca Bishop
- 5 years ago
- Views:
Transcription
1 Arile Ieraioal Joral of Moder Mahemaial Siee 4: 3-36 Ieraioal Joral of Moder Mahemaial Siee Joral homepage: ISSN: 66-86X Florida USA Modified Deompoiio Mehod for Solio of Fraioal Parial Differeial Eqaio of Two-Sided I. I. Gorial Deparme of Mahemai Ib Al Haiham College Edaio Baghdad Uiveriy Arile hiory: Reeived Ag Reeived i revied form 5 Sepember Aeped 7 Sepember Pblihed 8 Sepember. Abra: I hi paper a aalyial olio of he wo-ided fraioal parial differeial eqaio ha bee preeed. The algorihm for he aalyial olio for hi eqaio i baed o modified deompoiio mehod. The fraioal derivaive i deribed i Capo' ee. The aalyial mehod ha bee applied o olve a praial eample ad he rel have bee ompared wih he ea olio. Keyword: Modified deompoiio mehod Capo derivaive Fraioal parial differeial eqaio. Mahemai Sbje Claifiaio : 49M7. Irodio The fraioal all i ed i may field of iee ad egieerig [ 3]. The olio of differeial eqaio oaiig fraioal derivaive i mh ivolved ad i lai aalyi mehod are maily iegral raform h a aplae raform Forier raform Melli raform e.[4] I ree year Adomia deompoiio mehod i applied o olvig fraioal differeial eqaio. Thi mehod effiiely work for iiial vale or bodary vale problem for liear or oliear ordiary or parial differeial eqaio ad eve for ohai yem [5] a well. By ig hi mehod Saha Ray e al [6 7 8 ] olved liear differeial eqaio oaiig fraioal derivaive of order / or 3/ ad oliear differeial eqaio oaiig fraioal derivaive of order/. I hi paper we oider he wo-ided fraioal parial differeial eqaio of he form [3]: Copyrigh by Moder Sieifi Pre Compay Florida USA
2 I. J. Moder Mah. Si. 4: 3-36 Copyrigh by Moder Sieifi Pre Compay Florida USA 3 bje o he iiial odiio = f R ad he bodary odiio = k T R = k T where + - ad are kow fio of ad f i a kow fio of k ad k are kow fio of ad i a give fraioal mber. Whe = ad eq. beome he followig laial paraboli parial differeial eqaio: Similarly whe = ad eq. rede o he followig laial hyperboli parial differeial eqaio I he pree work we apply he modified deompoiio mehod for olvig eq. ad ompare he rel wih ea olio. The paper i orgaized a follow. Seio i he mahemaial ape; I Seio 3 i abo he bai idea of modified deompoiio mehod; I Seio 4he wo-ided fraioal parial differeial eqaio ad i olio by modified deompoiio mehod are preeed. I Seio 5 a merial eample i olved ig he modified deompoiio mehod. Fially he mmarized olio abo he olio of wo-ided fraioal parial differeial eqaio i i Seio 6.. Mahemaial Ape The mahemaial defiiio of fraioal all ha bee he bje of everal differe approahe [45]. The Capo fraioal derivaive operaor D of order i defied i he followig form:
3 I. J. Moder Mah. Si. 4: D f m m f m d where m m m. Similar o ieger-order differeiaio Capo fraioal derivaive operaor i a liear operaio: D f g D f D g where ad are oa. For he Capo' derivaive we have: D ad D R R R 3. Bai Idea of Modified Deompoiio Mehod Coider a geeral oliear eqaio [] R F g where i he operaor of he highe-ordered derivaive wih repe o ad R i he remaider of he liear operaor. The oliear erm i repreeed by F. Th we ge g R F 3 The ivere d i amed a iegral operaor give by The operaig wih he operaor o boh ide of Eqaio 3 we have f g R F 4 where f i he olio of homogeeo eqaio 5 Copyrigh by Moder Sieifi Pre Compay Florida USA
4 I. J. Moder Mah. Si. 4: ivolvig he oa of iegraio. The iegraio oa ivolved i he olio of homogeeo Eqaio 5 are o be deermied by he iiial or bodary odiio aordig a he problem i iiial-vale problem or bodary-vale problem. The ADM ame ha he kow fio a be epreed by a ifiie erie of he form ad he oliear operaor F a be deompoed by a ifiie erie of polyomial give by F A where will be deermied rerrely ad A are he o-alled polyomial of defied by A d F! d i i B he modified deompoiio mehod wa iroded by Wazwaz [9]. Thi mehod i baed o he ampio ha he fio f a be divided io wo par amely f ad f. Uder hi ampio we e f f f We apply hi deompoiio whe he fio f oi of everal par ad a be deompoed io wo differe par. I hi ae f i ally a mmaio of a polyomial ad rigoomeri or raedeal fio. A proper hoie for he par f i impora. For he mehod o be more effiie we ele f a oe erm of f or a lea a mber of erm if poible ad f oi of he remaiig erm of f. 4. Modified Deompoiio Mehod for Solvig he Two-Sided Fraioal Parial Differeial Eqaio We adop modified deompoiio mehod for olvig Eqaio. I he ligh of hi mehod we ame ha Copyrigh by Moder Sieifi Pre Compay Florida USA
5 I. J. Moder Mah. Si. 4: 3-36 Copyrigh by Moder Sieifi Pre Compay Florida USA 34 Now Eqaio a be rewrie a where whih i a eaily iverible liear operaor ad are he Capo derivaive of order. Therefore we a wrie The he modified deompoiio mehod MDM rerive heme i a follow f f 5. Nmerial Appliaio I hi eio we apply modified deompoiio mehod for fidig he aalyial olio of wo-ided fraioal parial differeial eqaio:
6 I. J. Moder Mah. Si. 4: Wih he oeffiie fio:.5 ad e. 8 e ad he ore fio: bje o he iiial odiio =.4 ad bodary odiio = ad.4 =.8e. Noe ha he ea olio o hi problem i: = e. Table how he aalyial olio for wo-ided fraioal parial differeial eqaio obaied for differe vale ad ompario bewee ea olio ad aalyial olio. Table. Compario bewee ea olio ad aalyial olio whe. 5 for wo-ided fraioal parial differeial eqaio Ea Solio Modified Adomia Deompoiio Mehod e - MADM Colio I hi paper aalyial olio for fraioal wo-ided fraioal parial differeial eqaio obaied by ig modified deompoiio mehod ha bee deribed ad demoraed. I i lear ha he modified deompoiio mehod i i high agreeme wih he ea olio. Copyrigh by Moder Sieifi Pre Compay Florida USA
7 I. J. Moder Mah. Si. 4: Referee [] Podlby I. Fraioal Differeial Eqaio Aademi Pre Sa Diego 999. [] Miller KS Ro B. A Irodio o he Fraioal Call ad Fraioal Differeial Eqaio Wiley New York 993. [3] Shimiz N Zhag W. Fraioal all approah o dyami problem of vioelai maerial JSME Serie C Mehaial Syem Mahie Eleme ad Mafarig 4999: [4] Da J. S. Time ad pae fraioal parial differeial eqaio J. Mah. Phy 465: [5] Adomia G. Noliear Sohai Operaor Eqaio Aademi Pre New York 986. [6] Saha R. S. Poddar B. P; Bera R.K. Aalyial olio of a dyami yem oaiig fraioal derivaive of order / by Adomia deompoiio mehod ASMEJ ApplMeh 75: [7] Saha R. S. Bera R.K. Aalyial olio of he Bagley Torvik eqaio by Adomia deompoiio mehod Appl. Mah. Comp. 685: [8] Saha R. S. Bera R.K. A approimae olio of a oliear fraioal differeial eqaio by Adomiade ompoiio mehod Appl. Mah. Comp. 675: [9] Wazwaz A. A reliable modifiaio of Adomia deompoiio mehod Appl. Mah. Comp. 999: [] Khader M. M. O he merial olio for he fraioal diffio eqaio Commiaio i Noliear Siee ad Nmerial Simlaio 6: [] Ray S. S. Aalyial olio for he pae fraioal diffio eqaio by wo-ep Adomia deompoiio mehod Comm. Noliear. Si. Nmer. Siml. 449: [] Wazwaz A. M. A reliable reame for mied Volerra-Fredholm iegral eqaio Applied Mahemai ad Compaio 7: [3] Meerhaer M. ad Tadjera C. Fiie Differee Approimaio for Two- Sided Spae- Fraioal Parial Differeial Eqaio Appl. Nmer. Mah. 566: 8-9. [4] Oldham K. B.ad SpaierJ. Fraioal Call: Theory ad Appliaio Differeiaio ad Iegraio o Arbirary Order Aademi Pre I. New York-odo 974. [5] Podlby I. A Irodio o Fraioal Derivaive Fraioal Differeial Eqaio Some Mehod of Their Solio ad Some of Their Appliaio Fraioal Differeial Eqaio Mahemai i Siee ad Egieerig Vol. 98 Aademi Pre Sa Diego 999. Copyrigh by Moder Sieifi Pre Compay Florida USA
A modified method for solving Delay differential equations of fractional order
IOSR Joural of Mahemais (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 3 Ver. VII (May. - Ju. 6), PP 5- www.iosrjourals.org A modified mehod for solvig Delay differeial equaios of fraioal order
Results on Existence and Uniqueness of Solution Of Impulsive Neutral Integro-Differential System
oral of Mahemai eearh; Vol No 4; A 8 SSN 96-9795 E-SSN 96-989 Pblihed by Caadia Ceer of Siee ad Edaio el o Eiee ad Uiqee of Solio Of mplie Neral ero-differeial Syem obi Dodi K & Ae ao E Deparme of Mahemai/Saii
A Comparative Study of Adomain Decompostion Method and He-Laplace Method
Applied Mahemaic,, 5, 5-6 Publihed Olie December i SciRe. hp://www.cirp.org/joural/am hp://d.doi.org/.6/am..5 A Comparaive Sudy of Adomai Decompoio Mehod ad He-Laplace Mehod Badradee A. A. Adam, Deparme
Comparison between Fourier and Corrected Fourier Series Methods
Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1
MODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC
Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations
Adaces i Pre Mahemaics,,, 7- hp://d.doi.org/.46/apm..45 Pblished Olie May (hp://www.scirp.org/joral/apm) Mire of a New Iegral Trasform ad omoopy Perrbaio Mehod for Solig Noliear Parial Differeial Eqaios
TIME RESPONSE Introduction
TIME RESPONSE Iroducio Time repoe of a corol yem i a udy o how he oupu variable chage whe a ypical e ipu igal i give o he yem. The commoly e ipu igal are hoe of ep fucio, impule fucio, ramp fucio ad iuoidal
Approximating Solutions for Ginzburg Landau Equation by HPM and ADM
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 193-9466 Vol. 5, No. Issue (December 1), pp. 575 584 (Previously, Vol. 5, Issue 1, pp. 167 1681) Applicaios ad Applied Mahemaics: A Ieraioal Joural
UNIT 1: ANALYTICAL METHODS FOR ENGINEERS
UNIT : ANALYTICAL METHODS FOR ENGINEERS Ui code: A// QCF Level: Credi vale: OUTCOME TUTORIAL SERIES Ui coe Be able o aalyse ad model egieerig siaios ad solve problems sig algebraic mehods Algebraic mehods:
On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He's Homotopy Perturbation Method
Available a hp://pvam.ed/aam Appl. Appl. Mah. ISSN: 93-9466 Special Isse No. (Ags ) pp. Applicaios ad Applied Mahemaics: A Ieraioal Joral (AAM) O Nmerical Solios of Two-Dimesioal Bossiesq Eqaios by Usig
A New Method to Detect and Correct the Critical Errors and Determine the Software-Reliability in Critical Software-System
Joral of Phyi: oferee Serie A New Mehod o Dee ad orre he riial Error ad Deermie he Sofware-Reliabiliy i riial Sofware-Syem To e hi arile: Omae Krii ad Joef Börök J. Phy.: of. Ser. 6 57 View he arile olie
VARIATIONAL ITERATION TRANSFORM METHOD FOR SOLVING BURGER AND COUPLED BURGER S EQUATIONS
VARIATIONAL ITERATION TRANSFORM METHOD FOR SOLVING BURGER AND COUPLED BURGER S EQUATIONS Ali Al-Fayadh ad Haa Ali Khawwa Deparme of Mahemaic ad Compuer Applicaio, College of Sciece, Al-Nahrai Uiveriy,
New Applications of Adomian Decomposition Method. Emad A. Az-Zo'bi
Middle-Eas Joral of Scieific Research (): 75-7 5 ISSN 99-9 IDOSI Pblicaios 5 DOI:.589/idosi.mejsr.5... New Applicaios of Adomia Decomposiio Mehod Emad A. Az-Zo'bi Deparme of Mahemaics ad Saisics Mah Uiversiy
Numerical KDV equation by the Adomian decomposition method
America Joral o oder Physics ; () : -5 Pblished olie ay (hp://wwwsciecepblishiggropcom/j/ajmp) doi: 648/jajmp merical KDV eqaio by he Adomia decomposiio mehod Adi B Sedra Uiversié Ib Toail Faclé des Scieces
International journal of Engineering Research-Online A Peer Reviewed International Journal Articles available online
Ieraioal joral of Egieerig Reearch-Olie Peer Reviewed Ieraioal Joral ricle available olie h://www.ijoer.i Vol.1. Ie.4. 01 RESERCH RTICLE ON TERNRY QUDRTIC EQUTION M..GOPLN S.VIDHYLKSHMI S.NIVETHITH Dearme
VARIATIONAL ITERATION METHOD: A COMPUTATIONAL TOOL FOR SOLVING COUPLED SYSTEM OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
Joral of Sciece a Ars Year 6 No. 336 pp. 43-48 6 ORIGINAL PAPER ARIATIONAL ITERATION METHOD: A COMPTATIONAL TOOL FOR SOLING COPLED SYSTEM OF NONLINEAR PARTIAL DIFFERENTIAL EQATIONS MORF OYEDNSI OLAYIOLA
Adomian Decomposition Method and its. Modification for Nonlinear. Abel's Integral Equation
I. Joral of Mah. Aalysis, Vol. 7,, o. 4, 49-5 HIKARI d, www.m-hikari.com hp://d.doi.org/.9/ijma..779 Adomia Decomposiio Mehod ad is Modificaio for Noliear Abel's Iegral Eqaio R. H. Kha ad H. O. Bakodah
The modified Exp-function method and its applications to the generalized K(n,n) and BBM equations with variable coefficients
IJST () A3 (Special isse-mahemaics): 359-365 Iraia Joral of Sciece & Techology hp://www.shiraz.ac.ir/e The modified Ep-fcio mehod ad is applicaios o he geeralized K() ad BBM eqaios wih varile coefficies
Turing-Computability of Solution of Hirota Equation Dianchen Lu1, a and Liming Fu1, b
Ieraioal Coferece o Comper Sciece a Elecroic Techology (ICCSET ) Trig-Compailiy of Solio of iroa Eqaio Diache L a a Limig F Facly of Sciece Jiag Uiveriy Zheiag Jiag 3P..Chia a Email: cl@.e.c Email: 6786997@qq.com
INTEGER INTERVAL VALUE OF NEWTON DIVIDED DIFFERENCE AND FORWARD AND BACKWARD INTERPOLATION FORMULA
Volume 8 No. 8, 45-54 ISSN: 34-3395 (o-lie versio) url: hp://www.ijpam.eu ijpam.eu INTEGER INTERVAL VALUE OF NEWTON DIVIDED DIFFERENCE AND FORWARD AND BACKWARD INTERPOLATION FORMULA A.Arul dass M.Dhaapal
PIECEWISE N TH ORDER ADOMIAN POLYNOMIAL STIFF DIFFERENTIAL EQUATION SOLVER 13
Abrac PIECEWISE N TH ORDER ADOMIAN POLYNOMIAL A piecewie h order Adomia polyomial olver for iiial value differeial equaio capable of olvig highly iff problem i preeed here. Thi powerful echique which employ
On the Existence and Uniqueness of Solutions for. Q-Fractional Boundary Value Problem
I Joural of ah Aalysis, Vol 5, 2, o 33, 69-63 O he Eisee ad Uiueess of Soluios for Q-Fraioal Boudary Value Prolem ousafa El-Shahed Deparme of ahemais, College of Eduaio Qassim Uiversiy PO Bo 377 Uizah,
On the Effective Region of Convergence of the Decomposition Series Solution
Joral of Algorihms & Compaioal Techology Vol. 7 No. 7 O he Effecive Regio of Covergece of he Decomposiio Series Solio J-Sheg Da a,b *, Radolph Rach c,, Zhog Wag a a School of Mahemaics ad Iformaio Scieces,
Math 2414 Homework Set 7 Solutions 10 Points
Mah Homework Se 7 Soluios 0 Pois #. ( ps) Firs verify ha we ca use he iegral es. The erms are clearly posiive (he epoeial is always posiive ad + is posiive if >, which i is i his case). For decreasig we
CHAPTER 2 Quadratic diophantine equations with two unknowns
CHAPTER - QUADRATIC DIOPHANTINE EQUATIONS WITH TWO UNKNOWNS 3 CHAPTER Quadraic diophaie equaio wih wo ukow Thi chaper coi of hree ecio. I ecio (A), o rivial iegral oluio of he biar quadraic diophaie equaio
A Note on Integral Transforms and Differential Equations
Malaysia Joral of Mahemaical Scieces 6(S): -8 () Special Ediio of Ieraioal Workshop o Mahemaical Aalysis (IWOMA) A Noe o Iegral Trasforms ad Differeial Eqaios, Adem Kilicma, 3 Hassa Elayeb ad, Ma Rofa
On The Geometrıc Interpretatıons of The Kleın-Gordon Equatıon And Solution of The Equation by Homotopy Perturbation Method
Available a hp://pvam.ed/aam Appl. Appl. Mah. SSN: 9-9466 Vol. 7, sse (December ), pp. 69-65 Applicaios ad Applied Mahemaics: A eraioal Joral (AAM) O The Geomerıc erpreaıos of The Kleı-Gordo Eqaıo Ad Solio
Variational Iteration Method for Solving Differential Equations with Piecewise Constant Arguments
I.J. Egieerig ad Maufacurig, 1,, 36-43 Publihed Olie April 1 i MECS (hp://www.mec-pre.e) DOI: 1.5815/ijem.1..6 Available olie a hp://www.mec-pre.e/ijem Variaioal Ieraio Mehod for Solvig Differeial Equaio
The Solution of the One Species Lotka-Volterra Equation Using Variational Iteration Method ABSTRACT INTRODUCTION
Malaysia Joural of Mahemaical Scieces 2(2): 55-6 (28) The Soluio of he Oe Species Loka-Volerra Equaio Usig Variaioal Ieraio Mehod B. Baiha, M.S.M. Noorai, I. Hashim School of Mahemaical Scieces, Uiversii
M-Point Boundary Value Problem for Caputo Fractional Differential Eqautions
OSR Joral o Egieerig OSRJEN SSN e: 5- SSN p: 78-879 Vol. 6 e ebrar. 6 V PP -7 www.iorje.org -Poi Bodar Vale Proble or Capo raioal Diereial Eaio J.A.Naware Depare o aheai Shririha ahaidalaa Gjoi- 65 Di.Oaabad.SNDA
A TAUBERIAN THEOREM FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY
U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 2, 206 ISSN 223-7027 A TAUBERIAN THEOREM FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY İbrahim Çaak I his paper we obai a Tauberia codiio i erms of he weighed classical
N! AND THE GAMMA FUNCTION
N! AND THE GAMMA FUNCTION Cosider he produc of he firs posiive iegers- 3 4 5 6 (-) =! Oe calls his produc he facorial ad has ha produc of he firs five iegers equals 5!=0. Direcly relaed o he discree! fucio
LYAPUNOV-KRASOVSKII STABILITY THEOREM FOR FRACTIONAL SYSTEMS WITH DELAY
LYAPUNOV-KRASOVSKII STABILITY THEOREM FOR FRACTIONAL SYSTEMS WITH DELAY D. BALEANU 12 A. RANJBAR N. 3 S.J. SADATI R. 3 H. DELAVARI 3 T. ABDELJAWAD 1 (MARAABA) V. GEJJİ 4 1 Deparme of Mahemais ad Compuer
DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR
Bllei UASVM, Horilre 65(/008 pissn 1843-554; eissn 1843-5394 DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR Crii C. MERCE Uiveriy of Agrilrl iee d Veeriry Mediie Clj-Npo,
Frequency Transformation in Digital Domain
Freqey Traormaio i Digia Domai Pho S. Ngye Mebore, Vioria, Araia Emai: gyeipho@reqeyraorm.om Abra Thi paper irode a ew agorihm o raorm a digia ow-pa ier io a digia ow-pa, high-pa, b-pa, b-op arrow-b ier
1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
SOLVING OF THE FRACTIONAL NON-LINEAR AND LINEAR SCHRÖDINGER EQUATIONS BY HOMOTOPY PERTURBATION METHOD
SOLVING OF THE FRACTIONAL NON-LINEAR AND LINEAR SCHRÖDINGER EQUATIONS BY HOMOTOPY PERTURBATION METHOD DUMITRU BALEANU, ALIREZA K. GOLMANKHANEH,3, ALI K. GOLMANKHANEH 3 Deparme of Mahemaics ad Compuer Sciece,
Local Fractional Variational Iteration Method for Solving Nonlinear Partial Differential Equations within Local Fractional Operators
Available a hp://pvamed/aam Appl Appl Mah SSN: 93-9466 Vol sse December 5 pp 55-65 Applicaios ad Applied Mahemaics: A eraioal Joral AAM Local Fracioal Variaioal eraio Mehod for Solvig Noliear Parial Differeial
On Similarity Transformations A Classical Approach
O Similari rasformaios A Classial Aroah Edard M. Rose EMR eholo Gro Irodio Similari rasformaios are ofe ilized o oer arial differeial eqaios o a se of ordiar differeial eqaios []. he ordiar differeial
Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions
IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics
Homotopy Analysis Method for Solving Fractional Sturm-Liouville Problems
Ausralia Joural of Basic ad Applied Scieces, 4(1): 518-57, 1 ISSN 1991-8178 Homoopy Aalysis Mehod for Solvig Fracioal Surm-Liouville Problems 1 A Neamay, R Darzi, A Dabbaghia 1 Deparme of Mahemaics, Uiversiy
Applying Differential Transformation Method to. the One-Dimensional Planar Bratu Problem
It J Cotemp Math Siees, Vol, 7, o, 49-54 Applyig Differetial Trasformatio Method to the Oe-Dimesioal Plaar Brat Problem I H Abdel-Halim Hassa Departmet of Mathematis, Falty of Siee, Zagazig iversity, Zagazig,
Compact Finite Difference Schemes for Solving a Class of Weakly- Singular Partial Integro-differential Equations
Ma. Sci. Le. Vol. No. 53-0 (0 Maemaical Scieces Leers A Ieraioal Joural @ 0 NSP Naural Scieces Publisig Cor. Compac Fiie Differece Scemes for Solvig a Class of Weakly- Sigular Parial Iegro-differeial Equaios
Frequency Transformation in Digital Domain
Ieraioa Jora o Siga Proeig Syem Vo. 4, o. 5, Oober 6 Freqey raormaio i Digia Domai Pho S. gye Deparme o Commiaio Iormai, Vioria iveriy o ehoogy, Mebore, Araia Emai: gyeipho@reqeyraorm.om Eqaio () a be
K3 p K2 p Kp 0 p 2 p 3 p
Mah 80-00 Mo Ar 0 Chaer 9 Fourier Series ad alicaios o differeial equaios (ad arial differeial equaios) 9.-9. Fourier series defiiio ad covergece. The idea of Fourier series is relaed o he liear algebra
The analysis of the method on the one variable function s limit Ke Wu
Ieraioal Coferece o Advaces i Mechaical Egieerig ad Idusrial Iformaics (AMEII 5) The aalysis of he mehod o he oe variable fucio s i Ke Wu Deparme of Mahemaics ad Saisics Zaozhuag Uiversiy Zaozhuag 776
Review Exercises for Chapter 9
0_090R.qd //0 : PM Page 88 88 CHAPTER 9 Ifiie Series I Eercises ad, wrie a epressio for he h erm of he sequece..,., 5, 0,,,, 0,... 7,... I Eercises, mach he sequece wih is graph. [The graphs are labeled
Numerical Solution of Parabolic Volterra Integro-Differential Equations via Backward-Euler Scheme
America Joural of Compuaioal ad Applied Maemaics, (6): 77-8 DOI:.59/.acam.6. Numerical Soluio of Parabolic Volerra Iegro-Differeial Equaios via Bacward-Euler Sceme Ali Filiz Deparme of Maemaics, Ada Mederes
Hadamard matrices from the Multiplication Table of the Finite Fields
adamard marice from he Muliplicaio Table of he Fiie Field 신민호 송홍엽 노종선 * Iroducio adamard mari biary m-equece New Corucio Coe Theorem. Corucio wih caoical bai Theorem. Corucio wih ay bai Remark adamard
Extended Laguerre Polynomials
I J Coemp Mah Scieces, Vol 7, 1, o, 189 194 Exeded Laguerre Polyomials Ada Kha Naioal College of Busiess Admiisraio ad Ecoomics Gulberg-III, Lahore, Pakisa adakhaariq@gmailcom G M Habibullah Naioal College
Application of the Adomian Decomposition Method (ADM) and the SOME BLAISE ABBO (SBA) method to solving the diffusion-reaction equations
Advaces i Theoreical ad Alied Mahemaics ISSN 973-4554 Volume 9, Number (4),. 97-4 Research Idia Publicaios h://www.riublicaio.com Alicaio of he Adomia Decomosiio Mehod (ADM) ad he SOME BLAISE ABBO (SBA)
Available online at J. Math. Comput. Sci. 4 (2014), No. 4, ISSN:
Available olie a hp://sci.org J. Mah. Compu. Sci. 4 (2014), No. 4, 716-727 ISSN: 1927-5307 ON ITERATIVE TECHNIQUES FOR NUMERICAL SOLUTIONS OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS S.O. EDEKI *, A.A.
A Comparative Study of Variational Iteration Method and He-Laplace Method
Applied Mahemaic,,, 9- hp://d.doi.org/./am..7 Publihed Olie Ocober (hp://www.scirp.org/joural/am) A Comparaive Sud of Variaioal Ieraio Mehod ad He-Laplace Mehod Hradeh Kumar Mihra Deparme of Mahemaic,
REDUCED DIFFERENTIAL TRANSFORM METHOD FOR GENERALIZED KDV EQUATIONS. Yıldıray Keskin and Galip Oturanç
Mahemaical ad Compuaioal Applicaios, Vol. 15, No. 3, pp. 38-393, 1. Associaio for Scieific Research REDUCED DIFFERENTIAL TRANSFORM METHOD FOR GENERALIZED KDV EQUATIONS Yıldıray Kesi ad Galip Ouraç Deparme
2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)
Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he
A comparative Study of Variational Iteration Method and He-Laplace Method
Shiraz Uiveri of Techolog From he SelecedWork of Habibolla Laifizadeh A comparaive Sud of Variaioal Ieraio Mehod ad He-Laplace Mehod Habibolla Laifizadeh, Shiraz Uiveri of Techolog Available a: hp://work.bepre.com/habib_laifizadeh/95/
APPROXIMATE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH UNCERTAINTY
APPROXIMATE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH UNCERTAINTY ZHEN-GUO DENG ad GUO-CHENG WU 2, 3 * School of Mahemaics ad Iformaio Sciece, Guagi Uiversiy, Naig 534, PR Chia 2 Key Laboraory
A Novel Approach for Solving Burger s Equation
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 93-9466 Vol. 9, Issue (December 4), pp. 54-55 Applicaios ad Applied Mahemaics: A Ieraioal Joural (AAM) A Novel Approach for Solvig Burger s Equaio
Ruled surfaces are one of the most important topics of differential geometry. The
CONSTANT ANGLE RULED SURFACES IN EUCLIDEAN SPACES Yuuf YAYLI Ere ZIPLAR Deparme of Mahemaic Faculy of Sciece Uieriy of Aara Tadoğa Aara Turey yayli@cieceaaraedur Deparme of Mahemaic Faculy of Sciece Uieriy
A Generalization of Hermite Polynomials
Ieraioal Mahemaical Forum, Vol. 8, 213, o. 15, 71-76 HIKARI Ld, www.m-hikari.com A Geeralizaio of Hermie Polyomials G. M. Habibullah Naioal College of Busiess Admiisraio & Ecoomics Gulberg-III, Lahore,
ME 321 Kinematics and Dynamics of Machines S. Lambert Winter 2002
ME 31 Kiemaic ad Dyamic o Machie S. Lamber Wier 6.. Forced Vibraio wih Dampig Coider ow he cae o orced vibraio wih dampig. Recall ha he goverig diereial equaio i: m && c& k F() ad ha we will aume ha he
Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations
Ieraioal Joural of Modelig ad Opimizaio, Vol. 4, No. 4, Augus 4 Compariso of Adomia Decomposiio Mehod ad Taylor Mari Mehod i Solvig Differe Kids of Parial Differeial Equaios Sia Deiz ad Necde Bildik Absrac
Research Article The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method
Absrac ad Applied Aalysis Volme 3, Aricle ID 3875, 6 pages hp://dx.doi.org/.55/3/3875 Research Aricle The Aalyical Solio of Some Fracioal Ordiary Differeial Eqaios by he Smd Trasform Mehod Hasa Bl, Haci
Calculus BC 2015 Scoring Guidelines
AP Calculus BC 5 Scorig Guidelies 5 The College Board. College Board, Advaced Placeme Program, AP, AP Ceral, ad he acor logo are regisered rademarks of he College Board. AP Ceral is he official olie home
The Inverse of Power Series and the Partial Bell Polynomials
1 2 3 47 6 23 11 Joural of Ieger Sequece Vol 15 2012 Aricle 1237 The Ivere of Power Serie ad he Parial Bell Polyomial Miloud Mihoubi 1 ad Rachida Mahdid 1 Faculy of Mahemaic Uiveriy of Sciece ad Techology
Theoretical Physics Prof. Ruiz, UNC Asheville, doctorphys on YouTube Chapter Q Notes. Laplace Transforms. Q1. The Laplace Transform.
Theoreical Phyic Prof. Ruiz, UNC Aheville, docorphy o YouTue Chaper Q Noe. Laplace Traform Q1. The Laplace Traform. Pierre-Simo Laplace (1749-187) Courey School of Mhemic ad Siic Uiveriy of S. Adrew, Scolad
S n. = n. Sum of first n terms of an A. P is
PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.
EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
What is a Communications System?
Wha is a ommuiaios Sysem? Aual Real Life Messae Real Life Messae Replia Ipu Sial Oupu Sial Ipu rasduer Oupu rasduer Eleroi Sial rasmier rasmied Sial hael Reeived Sial Reeiver Eleroi Sial Noise ad Disorio
Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
America Joural of Compuaioal Mahemaics, 04, 4, 80-88 Published Olie Sepember 04 i SciRes. hp://www.scirp.org/joural/ajcm hp://dx.doi.org/0.436/ajcm.04.4404 Mea Square Coverge Fiie Differece Scheme for
VARIOUS phenomena occurring in the applied sciences
roceedigs of he Ieraioal MuliCoferece of Egieers ad Compuer Scieiss 8 Vol I IMECS 8 March -6 8 Hog Kog Exac Soluios ad Numerical Compariso of Mehods for Solvig Fracioal-Order Differeial Sysems Nachapo
Research Article A Generalized Nonlinear Sum-Difference Inequality of Product Form
Joural of Applied Mahemaics Volume 03, Aricle ID 47585, 7 pages hp://dx.doi.org/0.55/03/47585 Research Aricle A Geeralized Noliear Sum-Differece Iequaliy of Produc Form YogZhou Qi ad Wu-Sheg Wag School
BE.430 Tutorial: Linear Operator Theory and Eigenfunction Expansion
BE.43 Tuorial: Liear Operaor Theory ad Eigefucio Expasio (adaped fro Douglas Lauffeburger) 9//4 Moivaig proble I class, we ecouered parial differeial equaios describig rasie syses wih cheical diffusio.
FIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE
Mohia & Samaa, Vol. 1, No. II, December, 016, pp 34-49. ORIGINAL RESEARCH ARTICLE OPEN ACCESS FIED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE 1 Mohia S. *, Samaa T. K. 1 Deparme of Mahemaics, Sudhir Memorial
Communications II Lecture 4: Effects of Noise on AM. Professor Kin K. Leung EEE and Computing Departments Imperial College London Copyright reserved
Commuiaio II Leure 4: Effe of Noie o M Profeor Ki K. Leug EEE ad Compuig Deparme Imperial College Lodo Copyrigh reerved Noie i alog Commuiaio Syem How do variou aalog modulaio heme perform i he preee of
arxiv:math/ v1 [math.fa] 1 Feb 1994
![arxiv:math/ v1 [math.fa] 1 Feb 1994](/thumbs/93/114291597.jpg "arxiv:math/ v1 [math.fa] 1 Feb 1994")
arxiv:mah/944v [mah.fa] Feb 994 ON THE EMBEDDING OF -CONCAVE ORLICZ SPACES INTO L Care Schü Abrac. I [K S ] i wa how ha Ave ( i a π(i) ) π i equivale o a Orlicz orm whoe Orlicz fucio i -cocave. Here we
On Another Type of Transform Called Rangaig Transform
Ieraioal Joural of Parial Differeial Equaios ad Applicaios, 7, Vol 5, No, 4-48 Available olie a hp://pubssciepubcom/ijpdea/5//6 Sciece ad Educaio Publishig DOI:69/ijpdea-5--6 O Aoher Type of Trasform Called
Extremal graph theory II: K t and K t,t
Exremal graph heory II: K ad K, Lecure Graph Theory 06 EPFL Frak de Zeeuw I his lecure, we geeralize he wo mai heorems from he las lecure, from riagles K 3 o complee graphs K, ad from squares K, o complee
Notes 03 largely plagiarized by %khc
1 1 Discree-Time Covoluio Noes 03 largely plagiarized by %khc Le s begi our discussio of covoluio i discree-ime, sice life is somewha easier i ha domai. We sar wih a sigal x[] ha will be he ipu io our
Curvilinear Motion: Normal and Tangential Components
15 Crviliear Moio: Noral ad Tageial Copoe Ref: Hibbeler 1.7, Bedford & Fowler: Dyaic.3 Whe he pah of a paricle i kow, a - coordiae ye wih a origi a he locaio of he paricle (a a ia i ie) ca be helpfl i
Prakash Chandra Rautaray 1, Ellipse 2
Prakash Chadra Rauara, Ellise / Ieraioal Joural of Egieerig Research ad Alicaios (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue, Jauar -Februar 3,.36-337 Degree Of Aroimaio Of Fucios B Modified Parial
The Structures of Fuzzifying Measure
Sesors & Trasduers Vol 7 Issue 5 May 04 pp 56-6 Sesors & Trasduers 04 by IFSA Publishig S L hp://wwwsesorsporalom The Sruures of Fuzzifyig Measure Shi Hua Luo Peg Che Qia Sheg Zhag Shool of Saisis Jiagxi
DETERMINATION OF PARTICULAR SOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS BY DISCRETE DECONVOLUTION
U.P.B. ci. Bull. eries A Vol. 69 No. 7 IN 3-77 DETERMINATION OF PARTIULAR OLUTION OF NONHOMOGENEOU LINEAR DIFFERENTIAL EQUATION BY DIRETE DEONVOLUTION M. I. ÎRNU e preziă o ouă meoă e eermiare a soluţiilor
MODIFIED ADOMIAN DECOMPOSITION METHOD FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS
Review of he Air Force Academy No 3 (3) 15 ODIFIED ADOIAN DECOPOSIION EHOD FOR SOLVING RICCAI DIFFERENIAL EQUAIONS 1. INRODUCION Adomia decomposiio mehod was foud by George Adomia ad has recely become
F D D D D F. smoothed value of the data including Y t the most recent data.
Module 2 Forecasig 1. Wha is forecasig? Forecasig is defied as esimaig he fuure value ha a parameer will ake. Mos scieific forecasig mehods forecas he fuure value usig pas daa. I Operaios Maageme forecasig
SUMMATION OF INFINITE SERIES REVISITED
SUMMATION OF INFINITE SERIES REVISITED I several aricles over he las decade o his web page we have show how o sum cerai iiie series icludig he geomeric series. We wa here o eed his discussio o he geeral
Using Linnik's Identity to Approximate the Prime Counting Function with the Logarithmic Integral
Usig Lii's Ideiy o Approimae he Prime Couig Fucio wih he Logarihmic Iegral Naha McKezie /26/2 aha@icecreambreafas.com Summary:This paper will show ha summig Lii's ideiy from 2 o ad arragig erms i a cerai
The Connection between the Basel Problem and a Special Integral
Applied Mahemaics 4 5 57-584 Published Olie Sepember 4 i SciRes hp://wwwscirporg/joural/am hp://ddoiorg/436/am45646 The Coecio bewee he Basel Problem ad a Special Iegral Haifeg Xu Jiuru Zhou School of
1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
ECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
SLOW INCREASING FUNCTIONS AND THEIR APPLICATIONS TO SOME PROBLEMS IN NUMBER THEORY
VOL. 8, NO. 7, JULY 03 ISSN 89-6608 ARPN Jourl of Egieerig d Applied Sciece 006-03 Ai Reerch Publihig Nework (ARPN). All righ reerved. www.rpjourl.com SLOW INCREASING FUNCTIONS AND THEIR APPLICATIONS TO
Common Solution of Nonlinear Functional Equations via Iterations
Proeedigs of he World Cogress o Egieerig Vol I WCE July 6-8 Lodo U.K. Coo Soluio of Noliear Fuioal Equaios via Ieraios Muhaad Arshad Akbar Aza ad Pasquale Vero Absra We obai oo fied ois ad ois of oiidee
A Study On (H, 1)(E, q) Product Summability Of Fourier Series And Its Conjugate Series
Mahemaical Theory ad Modelig ISSN 4-584 (Paper) ISSN 5-5 (Olie) Vol.7, No.5, 7 A Sudy O (H, )(E, q) Produc Summabiliy Of Fourier Series Ad Is Cojugae Series Sheela Verma, Kalpaa Saxea * Research Scholar
Basic Results in Functional Analysis
Preared by: F.. ewis Udaed: Suday, Augus 7, 4 Basic Resuls i Fucioal Aalysis f ( ): X Y is coiuous o X if X, (, ) z f( z) f( ) f ( ): X Y is uiformly coiuous o X if i is coiuous ad ( ) does o deed o. f
CHAPTER 2. Problem 2.1. Given: m k = k 1. Determine the weight of the table sec (b)
CHPTER Problem. Give: m T π 0. 5 sec (a) T m 50 g π. Deermie he weigh of he able. 075. sec (b) Taig he raio of Eq. (b) o Eq. (a) ad sqarig he resl gives or T T mg m 50 g m 50 5. 40 lbs 50 0.75. 5 m g 0.5.
DIFFERENCE EQUATIONS
DIFFERECE EQUATIOS Lier Cos-Coeffiie Differee Eqios Differee Eqios I disree-ime ssems, esseil feres of ip d op sigls pper ol speifi iss of ime, d he m o e defied ewee disree ime seps or he m e os. These
ME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
Application of Fixed Point Theorem of Convex-power Operators to Nonlinear Volterra Type Integral Equations
Ieraioal Mahemaical Forum, Vol 9, 4, o 9, 47-47 HIKRI Ld, wwwm-hikaricom h://dxdoiorg/988/imf4333 licaio of Fixed Poi Theorem of Covex-ower Oeraors o Noliear Volerra Tye Iegral Equaios Ya Chao-dog Huaiyi
ODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
David Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =