On generalized 2-step continuous linear multistep method of hybrid type for the integration of second order ordinary differential equations
|
|
|
- Shauna Ellis
- 5 years ago
- Views:
Transcription
1 Avlble onlne t Scolr Reerc brry Arcve o Apple Scence Reerc :- ttp://colrreerclbrry.co/rcve.tl ISSN 9-X CODEN USA AASRC9 On generlze -tep contnuou lner ulttep eto o ybr type or te ntegrton o econ orer ornry erentl equton J. O. Ege S. A. Ounug A. B. Sooluwe. A. Anb Deprtent o tetc Unverty o go Ao go Deprtent o Coputer Scence Unverty o go Ao go Deprtent o tetc go Stte Unverty Oo. go ABSTRACT: T pper propoe generlze -tep contnuou ulttep eto o ybr type or te rect ntegrton o econ-orer ornry erentl equton n ulttep collocton tecnque wc yel bloc eto. Te cee obtne ue ngle contnuou or wc erve ly o orul nvolvng uc tt on ubttuton o n o-tep pont b-ybr contnuou cee obtne. Te crete equvlent lo obtne tereter ro te contnuou ly o orul bloc eto. It w covere tt Nuercl cee o StÖrer-Cowell type were recovere v t tecnque. Te cee obtne pleente to generte te nuercl oluton to econ orer ornry erentl equton. Te reult obtne re copre wt te Renowne Nuerov eto nown to be o optl Keywor: Collocton Bloc eto ybr StÖrer-Cowell Nuerov Optl Orer INTRODUCTION ny el o pplcton notbly n Scence n Engneerng yel ntl vlue proble o Secon orer ornry erentl equton re o te or y y y y y y. ny o uc proble y not be ely olve nlytclly ence nuercl cee re evelope to olve.. Tee equton re uully reuce to yte o rt orer ornry erentl equton n nuercl eto o Frt Orer erentl equton re ue to olve te. ner ulttep eto re powerul nuercl eto or olvng Derentl equton. Soe reercer ve ttepte te oluton o. ung lner ulttep eto wtout reucton to yte o rt orer ornry erentl equton tey nclue Brown 9
2 bert 99 Kyoe Aee et l. Onuny et l. y et l 9 to enton ew. bert 9 lo cue bout n optl two tep eto clle te Nuerov eto. In our prevou pper we evelope generlze cee o contnuou lner ulttep eto CS o ybr type or olvng rt orer ornry erentl equton Ege et l.. Here we eten our reult to generlzng te oluton to Secon Orer ornry erentl equton v ulttep collocton tecnque. T eto elp to prove contnuou nuercl cee wc ccoote ll ybr pont o tt on ubttuton o n o-tep pont b-ybr cee obtne or te rect ntegrton o. wtout reucton to yte o erentl equton. In ecton we preent te teoretcl proceure ue generlzton or ll ce n t cl. In ecton te generlze eto erve pecl ce o te teoretcl proceure or. Eple o cee generte ro te generlze eto were erve n ecton. Te Scee generte were pleente on oe proble n ecton. Fnlly concluon n uture reerc re were lo tte.. Teoretcl Proceure:. Coner te yte y y y y y y y. Te Nuercl Soluton to. cn be obtne ung tep eplct ner ulttep eto o te or α y. or econ-orer erentl equton bert 9 but nce we re nterete n obtnng n ybr cee ybr pont n were ntrouce generlzton o ll ybr eto o t cl o tt. becoe α y. To obtn te CS or. t necery to ue te power ere were te. tep eto o t cl. et n n be nuber o nterpolton n collocton repectvely ten we ll ve equton o te or repreente n te tr below yte o
3 g g g g g. Were re erve n te nterpolton n collocton repectvely erve n Ounug et l 9 n p n g p re polynol o egree p..e p p n g p p Epreng. urter DA C A C D were A ϕ For ubttutng: n. we ll obtn α uc tt or ny pproprte vlue o new CS o ybr type generte n gven α were α α n T cn be ue to generte bloc eto on evluton o t n repectvely.
4 . Dervton o te Generlze eto or For uc tep ybr eto.e. ettng. et te b polynol to te proble. be gven. Interpoltng : n lo colloctng t : n We ll obtn te yte o equton epre by te tr. Solvng t yte o equton wt ple otwre. Te ybr ter w elye o to obtn generlze cee rter tn n nvul contnuou orul wc lte to prtculr vlue n y et l. 9. We obtn Subttutng n nto. we obtn
5 .. n t rt ervtve. evlute t n repectvely to obtn te generlze crete ybr cee ro. ] [ ] [.. wc nvolve uncton o te generlze contnuou orulton o cl o tep contnuou ybr cee wc yel te generlze crete bloc eto. on ubttuton o n pproprte vlue o Q. Slrly te ervtve. evlute t n repectvely to obtn generlze bloc cee
6 . wc ue to obtn ervtve vlue y preent n te n n n n y y n te n proble... Eple o cee erve ro te generlze contnuou cee We ll now ubttute nto te generlze CS. t we obtn te CS. Subttutng n te generlze crete bloc cee or evlutng. t n yel 9.b Subttutng gn nto te generlze CS. t we obtn te CS
7 . Subttutng n te generlze crete bloc cee or evlutng. t n yel 9.b wc re te cee erve n y et l 9. Alo ubttutng. t we obtn te CS Subttutng n te generlze crete bloc cee or evlutng. t n yel b
8 . Ipleentton o te eto To be ble to pleent tee bloc cee.. n.. ny Eplct cee were generte ere n bunnce v ulttep collocton tecnque to evlute trtng vlue. Tee cee were generte to prect oe o te vlue epecte n our cee. But tee cee re ue wt repect to te n ue. Altoug Tylor ere w ue to evlute te vlue or y..e n or y y y y y O!! y y y y y y re te ntl vlue gven n te proble... Note tt tt y n Nuercl Eple Four eple re olve to eontrte our erve eto or vlue o y beng te nuercl oluton t vlue. Our reult ro bloc eto... re copre wt te Nuerov eto wc o optl orer.. y y y y. Anlytcl Soluton: y Co Sn. y y y y. Anlytcl Soluton: y e. y y y y. Anlytcl Soluton: y y. y π π y y y. y Anlytcl Soluton: y Sn Nuercl Soluton n Tble o Error RESUTS y/ y/ y/ optl nlytcl Ey/ Ey/ Ey/ Eoptl......E.E.E.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.9E-.E- e 9
9 b Grp o Soluton n Br Crt o Error. Nuercl Soluton n Tble o Error y/ y/ y/ optl nlytcl Ey/ Ey/ Ey/ Eoptl......E.E.E.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.9E-.9E E-.E-.9E-.9E E-.E-.E-.E E-.E-.E-.E E-.E-.9E-.E- b Grp o Soluton n Br Crt o Error. Nuercl Soluton n Tble o Error y/ y/ y/ Optl y 9 nlytcl Ey/ Ey/ Ey/ Eoptl......E.E.E.E E-.E-.E-.E E-.E-.9E-.E E- 9.E-.E-.E E-.E-.E-.E E-.E-.E-.E E-.E-.E-.9E E-.E-.9E-.E E-.9E-.E-.E E-.E- 9.E-.E E-.E-.E-.E-
10 b Grp o Soluton n Br Crt o Error. Nuercl Soluton n Tble o Error y/ y/ y/ nlytcl Ey/ Ey/ Ey/ E.E.E E-9.E-9.E E-.9E-.E E-.99E-.E E-.E-.9E E-.E-.E E-.E-.E E-.E-.E E-.9E-.9E E-.E-.E E-.E-.E- b Grp o Soluton n Br Crt o Error. CONCUSION T pper eontrte te ervton o generlze contnuou lner ulttep eto or te rect ntegrton o econ orer ornry erentl equton wtout reucng t to yte o rt orer ornry erentl equton wc been te uul prctce. Alo te pper preente generlze cee wc generte everl bloc/prllel cee or ubttuton o vlue. Nuercl reult ow tt te cee generte converge better on oe proble tn te optl orer eto. Contnuou ner ulttep eto re el trtng becue eplct crete cee erve v collocton tecnque were ue to prect bot gr n o-gr pont. Snce tee eto nvolve n eplct enton t owever uggete tt n tonl ter n wll be e to obtn noter cl o ully plct bloc cee n uture pper. Alo tblty nly wll be crre out wc epecte to be epenent on t enble te coce o te bet eto tt ute proble.
11 REFERENCES [] Aee S. O. Onuny P. Sren U. W. n y. A. : Journl o Coputtonl n Apple tetc 9. [] Butcer J. C. : Nuercl eto or Ornry Derentl Equton Jon Wley n on New or. [] Ege J. O. Ounug S. A. n Sooluwe A. B. : Journl o Inttute o tetc & Coputer Scence Coputer Scence Ser. vol. No [] Ege J. O. Ounug S. A. n Sooluwe A. B. : Journl o Inttute o tetc n Coputer Scence Vol No 9 -. [] Ger C. W. 9: SIA J. o Nuercl Anly 9 -. [] Kyoe S. J. : An Iprove Nuerov eto or Drect Soluton o Generl Secon Orer Intl Vlue Proble o Ornry Equton Ntonl t Centre proceeng. [] bert J. D. 9: Coputtonl eto n Ornry Derentl Equton Jon Wley n on New or. [] Ounug S. A. n Onuny P. 9: An Accurte Collocton eto or Solvng ODE ASE Frnce. [9] Ounug S. A. n Onuny P. 9: A Collocton Tu eto or te Soluton o ODE Abcu. [] Ounug S. A. n Ege J. O. 9: Journl o Ngern tetcl Pyc. [] Onuny P. Awoye D. O. Jtor S. N. n Sren U. W. 99: J. Ng. t Soc.. [] Onuny P. Ftoun J. n Aeo B. O. : J. o t. Soc [] y. A. n Bu A.. 9: Arcn Journl o tetc n Coputer Scence reerc vol. 9.
v v at 1 2 d vit at v v 2a d
SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton
Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations
Cter. Runge-Kutt nd Order Metod or Ordnr Derentl Eutons Ater redng ts cter ou sould be ble to:. understnd te Runge-Kutt nd order metod or ordnr derentl eutons nd ow to use t to solve roblems. Wt s te Runge-Kutt
ORDINARY DIFFERENTIAL EQUATIONS
6 ORDINARY DIFFERENTIAL EQUATIONS Introducton Runge-Kutt Metods Mult-step Metods Sstem o Equtons Boundr Vlue Problems Crcterstc Vlue Problems Cpter 6 Ordnr Derentl Equtons / 6. Introducton In mn engneerng
Computation of Fifth Degree of Spline Function Model by Using C++ Programming
www.ijci.org 89 Computton o Ft Degree o plne Functon Model b Usng C Progrmmng Frdun K. Hml, Aln A. Abdull nd Knd M. Qdr Mtemtcs Dept, Unverst o ulmn, ulmn, IRAQ Mtemtcs Dept, Unverst o ulmn, ulmn, IRAQ
Let us look at a linear equation for a one-port network, for example some load with a reflection coefficient s, Figure L6.
ECEN 5004, prng 08 Actve Mcrowve Crcut Zoy Popovc, Unverty of Colordo, Boulder LECURE 5 IGNAL FLOW GRAPH FOR MICROWAVE CIRCUI ANALYI In mny text on mcrowve mplfer (e.g. the clc one by Gonzlez), gnl flow-grph
Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations
Dynm o Lnke Herrhe Contrne ynm The Fethertone equton Contrne ynm pply ore to one omponent, other omponent repotone, rom ner to r, to ty tne ontrnt F Contrne Boy Dynm Chpter 4 n: Mrth mpule-be Dynm Smulton
E-Companion: Mathematical Proofs
E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth
Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden
Poton nd Speed Control Lund Unverty, Seden Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton.
Chapter I Continuous Control Systems : A Review
Chpter I Contnuou Control Sytem : A Revew I.D. Lnu, G. Zto - "Dgtl Control Sytem" - Chpter Chpter. Contnuou Control Sytem : A Revew. Contnuou-tme Moel.. me Domn.. Frequency Domn..3 Stblty..4 me Repone..5
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
Numbers Related to Bernoulli-Goss Numbers
ursh Journl of Anlyss n Nuber heory, 4, Vol., No., -8 Avlble onlne t htt://ubs.sceub.co/tnt///4 Scence n Eucton Publshng OI:.69/tnt---4 Nubers Relte to Bernoull-Goss Nubers Mohe Oul ouh Benough * érteent
Finite Difference Formulae for Unequal Sub- Intervals Using Lagrange s Interpolation Formula
Int. Journal o Mat. Analyi, Vol., 9, no. 7, 85-87 Finite Dierence Formulae or Unequal Sub- Interval Uing Lagrange Interpolation Formula Aok K. Sing a and B. S. Badauria b Department o Matematic, Faculty
Improvements on Waring s Problem
Improvement on Warng Problem L An-Png Bejng, PR Chna apl@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th paper, we wll gve ome mprovement for Warng problem Keyword: Warng Problem,
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
Lecture 9-3/8/10-14 Spatial Description and Transformation
Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.
Lecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
APPROXIMATE SOLUTION OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS BY MEANS OF A NEW RATIONAL CHEBYSHEV COLLOCATION METHOD
thetcl nd oputtonl Applctons ol. 5 o. pp. 5-56. Assocton for Scentfc eserch APPOXIAE SOLUIO OF HIGHE ODE LIEA DIFFEEIAL EQUAIOS BY EAS OF A EW AIOAL HEBYSHE OLLOAIO EHOD Slh Ylçınbş * esrn Özso ehet Sezer
Lecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
8. INVERSE Z-TRANSFORM
8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere
Research Article Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations
Hndaw Publhng Corporaton Mathematcal Problem n Engneerng Volume 205, Artcle ID 893763, page http://dx.do.org/0.55/205/893763 Reearch Artcle Runge-Kutta Type Method for Drectly Solvng Specal Fourth-Order
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
Quadrilateral et Hexahedral Pseudo-conform Finite Elements
Qurlterl et Heerl seuo-conform Fnte Elements E. DUBACH R. LUCE J.M. THOMAS Lbortore e Mtémtques Applquées UMR 5 u Frnce GDR MoMs Métoes Numérques pour les Flues. rs écembre 6 Wt s te problem? Loss of conergence
AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION
AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o
MULTIPLE REGRESSION ANALYSIS For the Case of Two Regressors
MULTIPLE REGRESSION ANALYSIS For the Cae of Two Regreor In the followng note, leat-quare etmaton developed for multple regreon problem wth two eplanator varable, here called regreor (uch a n the Fat Food
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
Linear predictive coding
Liner predictive coding Thi ethod cobine liner proceing with clr quntiztion. The in ide of the ethod i to predict the vlue of the current ple by liner cobintion of previou lredy recontructed ple nd then
Harmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
Mile Maksić. Faculty of Mechnical Engineering, University of Niš, YU
FCT UNIVERSITTIS Seres: Mens utot Control nd Robots Vol N o 00 pp 79-8 STBILITY OF THE FREELY SUPPORTE RECTNGULR PLTE STRENGTHENE WITH THE TRNSVERZL PROPPING IN THE PLSTIC RNGE UC 56:597:607/0705 Mle Msć
On Pfaff s solution of the Pfaff problem
Zur Pfaff scen Lösung des Pfaff scen Probles Mat. Ann. 7 (880) 53-530. On Pfaff s soluton of te Pfaff proble By A. MAYER n Lepzg Translated by D. H. Delpenc Te way tat Pfaff adopted for te ntegraton of
SOLVING NONLINEAR OPTIMIZATION PROBLEMS BY MEANS OF THE NETWORK PROGRAMMING METHOD
Internatonal Sypou on Stocatc Model n Relalty Engneerng, Le Scence and Operaton Manageent (SMRLO'0) SOLVING NONLINEAR OPTIMIZATION PROBLEMS BY MEANS O THE NETWORK PROGRAMMING METHOD Vladr N. BURKOV Pro.,
1 Review: Volumes of Solids (Stewart )
Lecture : Some Bic Appliction of Te Integrl (Stewrt 6.,6.,.,.) ul Krin eview: Volume of Solid (Stewrt 6.-6.) ecll: we d provided two metod for determining te volume of olid of revolution. Te rt w by dic
ORDINARY DIFFERENTIAL EQUATIONS EULER S METHOD
Numercal Analss or Engneers German Jordanan Unverst ORDINARY DIFFERENTIAL EQUATIONS We wll eplore several metods o solvng rst order ordnar derental equatons (ODEs and we wll sow ow tese metods can be appled
Outline. Review Quadrilateral Equation. Review Linear φ i Quadrilateral. Review x and y Derivatives. Review φ Derivatives
E 5 Engneerng nlss ore on Fnte Eleents n ore on Fnte Eleents n Two Densons Two Densons Lrr Cretto echncl Engneerng 5 Senr n Engneerng nlss prl 7-9 9 Otlne Revew lst lectre Qrtc ss nctons n two ensons orer
Small signal analysis
Small gnal analy. ntroducton Let u conder the crcut hown n Fg., where the nonlnear retor decrbed by the equaton g v havng graphcal repreentaton hown n Fg.. ( G (t G v(t v Fg. Fg. a D current ource wherea
INTERPOLATION(1) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek
ELM Numercl Anlss Dr Muhrrem Mercmek INTEPOLATION ELM Numercl Anlss Some of the contents re dopted from Lurene V. Fusett, Appled Numercl Anlss usng MATLAB. Prentce Hll Inc., 999 ELM Numercl Anlss Dr Muhrrem
PHYS 100 Worked Examples Week 05: Newton s 2 nd Law
PHYS 00 Worked Eaple Week 05: ewton nd Law Poor Man Acceleroeter A drver hang an ar frehener fro ther rearvew rror wth a trng. When acceleratng onto the hghwa, the drver notce that the ar frehener ake
A Computational Method for Solving Two Point Boundary Value Problems of Order Four
Yoge Gupta et al, Int. J. Comp. Tec. Appl., Vol (5), - ISSN:9-09 A Computatonal Metod for Solvng Two Pont Boundary Value Problem of Order Four Yoge Gupta Department of Matematc Unted College of Engg and
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
ECEN 5807 Lecture 26
ECEN 5807 eture 6 HW 8 due v D Frdy, rh, 0 S eture 8 on Wed rh 0 wll be leture reorded n 0 he week of rh 5-9 Sprng brek, no le ody: Conlude pled-dt odelng of hghfrequeny ndutor dyn n pek urrentode ontrolled
ATTRIBUTE SELECTION AND INTRUSION DETECTION FOR KNOWLEDGE-BASED AUTHENTICATION SYSTEMS
TTRIBTE SELECTIO D ITRSIO DETECTIO FOR OWLEDGE-BSED THETICTIO SYSTES Drgn olć, Brnlv Vunovć, Ch guyen Fculty of Technology, nverty of Portouth nglee Buldng, nglee Rod, Portouth, Hnt, PO 3DJ nted ngdo [drgn.nolc,
10.3 The Quadratic Formula
. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti
Analysis of Variance and Design of Experiments-II
Anly of Vrne Degn of Experment-II MODULE VI LECTURE - 8 SPLIT-PLOT AND STRIP-PLOT DESIGNS Dr Shlbh Deprtment of Mthemt & Sttt Indn Inttute of Tehnology Knpur Tretment ontrt: Mn effet The uefulne of hvng
Lyapunov-type inequality for the Hadamard fractional boundary value problem on a general interval [a; b]; (1 6 a < b)
![Lyapunov-type inequality for the Hadamard fractional boundary value problem on a general interval [a; b]; (1 6 a < b)](/thumbs/91/105870616.jpg "Lyapunov-type inequality for the Hadamard fractional boundary value problem on a general interval [a; b]; (1 6 a < b)")
Lypunov-type inequlity for the Hdmrd frctionl boundry vlue problem on generl intervl [; b]; ( 6 < b) Zid Ldjl Deprtement of Mthemtic nd Computer Science, ICOSI Lbortory, Univerity of Khenchel, 40000, Algeri.
The Fundamental Theorem of Calculus Part 2, The Evaluation Part
AP Clculus AB 6.4 Funmentl Theorem of Clculus The Funmentl Theorem of Clculus hs two prts. These two prts tie together the concept of integrtion n ifferentition n is regre by some to by the most importnt
CISE 301: Numerical Methods Lecture 5, Topic 4 Least Squares, Curve Fitting
CISE 3: umercl Methods Lecture 5 Topc 4 Lest Squres Curve Fttng Dr. Amr Khouh Term Red Chpter 7 of the tetoo c Khouh CISE3_Topc4_Lest Squre Motvton Gven set of epermentl dt 3 5. 5.9 6.3 The reltonshp etween
International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August ISSN
Interntionl Journl of Scientific & Engineering Reerc Volume Iue 8 ugut- 68 ISSN 9-558 n Inventory Moel wit llowble Sortge Uing rpezoil Fuzzy Number P. Prvti He & ocite Profeor eprtment of Mtemtic ui- E
Chapter 8: Fast Convolution. Keshab K. Parhi
Cater 8: Fat Convoluton Keab K. Par Cater 8 Fat Convoluton Introducton Cook-Too Algort and Modfed Cook-Too Algort Wnograd Algort and Modfed Wnograd Algort Iterated Convoluton Cyclc Convoluton Degn of Fat
The Derivation of Implicit Second Derivative Method for Solving Second-Order Stiff Ordinary Differential Equations Odes.
IOSR Jourl o Mtetcs (IOSR-JM) e-issn: - p-issn: 9-6X. Volue Issue Ver. I (Mr. - Apr. ) PP - www.osrourls.org Te Dervto o Iplct Secod Dervtve Metod or Solvg Secod-Order St Ordr Deretl Equtos Odes. Y. Skwe
Chapter 5: Root Locus
Chater 5: Root Locu ey condton for Plottng Root Locu g n G Gven oen-loo tranfer functon G Charactertc equaton n g,,.., n Magntude Condton and Arguent Condton 5-3 Rule for Plottng Root Locu 5.3. Rule Rule
F l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c
L i f e t i m e M a n a g e m e n t o f F l a-b s ah s e d S S D s U s i n g R e c o v e r-a y w a r e D y n a m i c T h r o t t l i n g S u n g j i n L e, e T a e j i n K i m, K y u n g h o, Kainmd J
TELCOM 2130 Time Varying Queues. David Tipper Associate Professor Graduate Telecommunications and Networking Program University of Pittsburgh Slides 7
TELOM 3 Tme Vryng Queues Dvd Tpper Assote Professor Grdute Teleommuntons nd Networkng Progrm Unversty of Pttsburgh ldes 7 Tme Vryng Behvor Teletrff typlly hs lrge tme of dy vrtons Men number of lls per
Pythagorean triples. Leen Noordzij.
Pythagorean trple. Leen Noordz Dr.l.noordz@leennoordz.nl www.leennoordz.me Content A Roadmap for generatng Pythagorean Trple.... Pythagorean Trple.... 3 Dcuon Concluon.... 5 A Roadmap for generatng Pythagorean
Numerical investigation of the meshless radial basis integral equation method for solving 2D anisotropic potential problems
0 0 0 ercl nvetgton of the ehle rdl b ntegrl eqton ethod for olvng D notropc potentl proble En Hn Oo En Tt Oo Whye Teong Ang School of Engneerng Monh Unverty Mly Bndr Snwy 00 Selngor Mly School of Scence
Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum
Recall that there was ore to oton than just spee A ore coplete escrpton of oton s the concept of lnear oentu: p v (8.) Beng a prouct of a scalar () an a vector (v), oentu s a vector: p v p y v y p z v
SINGULARLY PERTURBED BOUNDARY VALUE. We consider the following singularly perturbed boundary value problem
Cater PARAETRIC QUITIC SPLIE SOLUTIO OR SIGULARLY PERTURBED BOUDARY VALUE PROBLES Introcton We conser te ollong snglarly ertrbe bonary vale roblem " L r r > an ere s a small ostve arameter st
CURVE FITTING LEAST SQUARES METHOD
Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued
Fitting a Polynomial to Heat Capacity as a Function of Temperature for Ag. Mathematical Background Document
Fttng Polynol to Het Cpcty s Functon of Teperture for Ag. thetcl Bckground Docuent by Theres Jul Zelnsk Deprtent of Chestry, edcl Technology, nd Physcs onouth Unversty West ong Brnch, J 7764-898 tzelns@onouth.edu
CENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s geometrcl concept rsng from prllel forces. Tus, onl prllel forces possess centrod. Centrod s tougt of s te pont were te wole wegt of pscl od or sstem of prtcles s lumped.
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
Exponents and Powers
EXPONENTS AND POWERS 9 Exponents nd Powers CHAPTER. Introduction Do you know? Mss of erth is 5,970,000,000,000, 000, 000, 000, 000 kg. We hve lredy lernt in erlier clss how to write such lrge nubers ore
1 cos. where v v sin. Range Equations: for an object that lands at the same height at which it starts. v sin 2 i. t g. and. sin g
SPH3UW Unt.5 Projectle Moton Pae 1 of 10 Note Phc Inventor Parabolc Moton curved oton n the hape of a parabola. In the drecton, the equaton of oton ha a t ter Projectle Moton the parabolc oton of an object,
Quick Visit to Bernoulli Land
Although we have een the Bernoull equaton and een t derved before, th next note how t dervaton for an uncopreble & nvcd flow. The dervaton follow that of Kuethe &Chow ot cloely (I lke t better than Anderon).
LECTURE 23 SYNCHRONOUS MACHINES (3)
ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURE 3 SYNCHRONOUS MACHINES (3) Acknowledgent-Thee hndout nd lecture note given in cl re bed on teril fro Prof. Peter Suer ECE 330 lecture note. Soe lide
Introduction to Robotics (Fag 3480)
Intouton to Robot (Fg 8) Vå Robet Woo (Hw Engneeeng n pple Sene-B) Ole Jkob Elle PhD (Mofe fo IFI/UIO) Føtemnuen II Inttutt fo Infomtkk Unvetetet Olo Sekjonlee Teknolog Intevenjonenteet Olo Unvetetkehu
WEYL MANIFOLDS WITH SEMI-SYMMETRIC CONNECTION. Füsun Ünal 1 and Aynur Uysal 2. Turkey.
Mateatca and Coputatona Appcaton, Vo. 0, No. 3, pp. 35-358, 005. Aocaton for centfc eearc WEYL MANIFOLD WITH EMI-YMMETIC CONNECTION Füun Üna and Aynur Uya Marara Unverty, Facuty of cence and Letter, Departent
A SIMPLE EQUATION FOR ICE SHEET THICKNESS AND ICE FORMATION/BREAKUP PREDICTION
Journl o JSCE, Vol. 2, 23-213, 214 A SIMPLE EQUATION FOR ICE SHEET THICKNESS AND ICE FORMATION/BREAKUP PREDICTION Yuro YOSHIKAWA 1, Yuru WATANABE 2 nd A ITOH 3,4 1 Member o JSCE, Atnt Proeor, Dept. o Cvl
Multivariate Time Series Analysis
Mulvre me Sere Anl Le { : } be Mulvre me ere. Denon: () = men vlue uncon o { : } = E[ ] or. (,) = Lgged covrnce mr o { : } = E{[ - ()][ - ()]'} or, Denon: e me ere { : } onr e jon drbuon o,,, e me e jon
M. Mechee, 1,2 N. Senu, 3 F. Ismail, 3 B. Nikouravan, 4 and Z. Siri Introduction
Hndaw Publhng Corporaton Mathematcal Problem n Engneerng Volume 23, Artcle ID 795397, 7 page http://dx.do.org/.55/23/795397 Reearch Artcle A Three-Stage Ffth-Order Runge-Kutta Method for Drectly Solvng
UNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR ON DOMAINS IN COMPLEX PROJECTIVE SPACES
wwwrresscom/volmes/vol7isse/ijrras_7 df UNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOIAL OPERATOR ON DOAINS IN COPLEX PROJECTIVE SPACES D Feng & L Ynl * Scool of emcs nd Pyscs Scence
Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed
Definition of Tracking
Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,
Method Of Fundamental Solutions For Modeling Electromagnetic Wave Scattering Problems
Internatonal Workhop on MehFree Method 003 1 Method Of Fundamental Soluton For Modelng lectromagnetc Wave Scatterng Problem Der-Lang Young (1) and Jhh-We Ruan (1) Abtract: In th paper we attempt to contruct
THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
NEAR NET SHAPE FORGING USING THE BACKWARD DEFORMATION METHOD
VII Internatonal Conference on Computatonal Platcty COMPLAS 2003 E. Oñate an D. R. J. Owen (E) CIMNE, Barcelona, 2003 NEAR NET SHAPE FORGING USING THE BACKWARD DEFORMATION METHOD Bglar F. R. *, Abrna K.
This appendix derives Equations (16) and (17) from Equations (12) and (13).
Capital growt pat of te neoclaical growt model Online Supporting Information Ti appendix derive Equation (6) and (7) from Equation () and (3). Equation () and (3) owed te evolution of pyical and uman capital
On the SO 2 Problem in Thermal Power Plants. 2.Two-steps chemical absorption modeling
Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : 557-56 Oct 5 On the SO Problem n Thermal Power Plant Two-tep chemcal aborpton modelng hr Boyadjev, P
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
Numerical Solution of Nonlinear Multi-order Fractional Differential Equations by Implementation of the Operational Matrix of Fractional Derivative
Studes n Nonlner Scences (): 5-, ISSN -9 IOSI Publctons, Numercl Soluton of Nonlner Mult-order Frctonl fferentl Equtons by Implementton of the Opertonl Mtr of Frctonl ervtve M.M. Khder eprtment of Mthemtcs,
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
When current flows through the armature, the magnetic fields create a torque. Torque = T =. K T i a
D Motor Bic he D pernent-gnet otor i odeled reitor ( ) in erie with n inductnce ( ) nd voltge ource tht depend on the ngulr velocity of the otor oltge generted inide the rture K ω (ω i ngulr velocity)
CHAPTER 5 DESIGN OF SPEED CONTROLLER FOR CONVERTER FED PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE
8 CHAPER 5 DESIN OF SPEED CONROLLER FOR CONVERER FED PERMANEN MANE SYNCHRONOUS MOOR DRIVE 5. INRODUCION he Penent Mgnet Synchonou Moto PMSM develop nuodl bck ef Pfff et l 98 etblhng telf eou copetto to
Numerical Methods using the Successive Approximations for the Solution of a Fredholm Integral Equation
ece Advce Appled d eorecl ec uercl eod u e Succeve Approo or e Soluo o Fredol Ierl Equo AIA OBIŢOIU epre o ec d opuer Scece Uvery o Peroş Uvery Sree 6 Peroş OAIA rdorou@yoo.co Arc: pper pree wo eod or
4-4 E-field Calculations using Coulomb s Law
1/11/5 ection_4_4_e-field_clcultion_uing_coulomb_lw_empty.doc 1/1 4-4 E-field Clcultion uing Coulomb Lw Reding Aignment: pp. 9-98 Specificlly: 1. HO: The Uniform, Infinite Line Chrge. HO: The Uniform Dik
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Calculate the efficiency associated with one rotation of the axle
We cn clculte the efficiency of one rottion of the xle by exining the work one. k Mx Your Rie: Workheet hi ctivity will tke you through the tep neee to optiize the work ue in your ouetrp cr. ollow thi
SAMPLE CSc 340 EXAM QUESTIONS WITH SOLUTIONS: part 2
AMPLE C EXAM UETION WITH OLUTION: prt. It n sown tt l / wr.7888l. I Φ nots orul or pprotng t vlu o tn t n sown tt t trunton rror o ts pproton s o t or or so onstnts ; tt s Not tt / L Φ L.. Φ.. /. /.. Φ..787.
System in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
EXERCISES FOR SECTION 6.3
y 6. Secon-Orer Equation 499.58 4 t EXERCISES FOR SECTION 6.. We ue integration by part twice to compute Lin ωt Firt, letting u in ωt an v e t t,weget Lin ωt in ωt e t e t lim b in ωt e t t. in ωt ω e
Shuai Dong. Isaac Newton. Gottfried Leibniz
Computatonal pyscs Sua Dong Isaac Newton Gottred Lebnz Numercal calculus poston dervatve ntegral v velocty dervatve ntegral a acceleraton Numercal calculus Numercal derentaton Numercal ntegraton Roots
mywbut.com Lesson 13 Representation of Sinusoidal Signal by a Phasor and Solution of Current in R-L-C Series Circuits
wut.co Lesson 3 Representtion of Sinusoil Signl Phsor n Solution of Current in R-L-C Series Circuits wut.co In the lst lesson, two points were escrie:. How sinusoil voltge wvefor (c) is generte?. How the
fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.
OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te
UNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY
UNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH HÖLDER CONTINUITY YIFEI PAN, MEI WANG, AND YU YAN ABSTRACT We estblish soe uniqueness results ner 0 for ordinry differentil equtions of the
Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano
RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson
APPENDIX 2 LAPLACE TRANSFORMS
APPENDIX LAPLACE TRANSFORMS Thi ppendix preent hort introduction to Lplce trnform, the bic tool ued in nlyzing continuou ytem in the frequency domin. The Lplce trnform convert liner ordinry differentil
Trigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245.
Trgonometry Trgonometry Solutons Currulum Redy CMMG:, 4, 4 www.mthlets.om Trgonometry Solutons Bss Pge questons. Identfy f the followng trngles re rght ngled or not. Trngles,, d, e re rght ngled ndted
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?
Model Fitting and Robust Regression Methods
Dertment o Comuter Engneerng Unverst o Clorn t Snt Cruz Model Fttng nd Robust Regresson Methods CMPE 64: Imge Anlss nd Comuter Vson H o Fttng lnes nd ellses to mge dt Dertment o Comuter Engneerng Unverst