Numerical solution of differential equations:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New Delhi u.a.
Wiley Eastern
1984
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 698 S. graph. Darst. |
| ISBN: | 0852264321 |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical solution of differential equations |
| 250 | |a 2. ed. | ||
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Datensatz im Suchindex
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| adam_text | Titel: Numerical solution of differential equations
Autor: Jain, Mahinder K
Jahr: 1984
CONTENTS Foreword Preface to the Second Edition Preface to the First Edition vii ix xi Chapter 1 . Elements of Ordinary Differential Initial Value 1.1 Introduction 1 1.2 Initial Value Problems 2 1.3 Difference Equations 3 1.4 Numerical Methods 7 1.5 Stability Analysis 12 Interval of absolute stability 1.6 Convergence Analysis 17 Bibliographical note Problems 2.1 Introduction 27 2.2 Taylor Series Method 28 Convergence 2.3 Runge-Kutta Methods 31 Second order methods Third order methods Fourth order methods High order Runge-Kutta methods Results from computations for Runge-Kutta methods Convergence Approximation of truncation error 2.4 Extrapolation Method 46 Euler extrapolation method 2.5 Stability Analysis 50 Fourth order Runge-Kutta method Euler extrapolation method Problem Approximation 1 Chapter 2. Singlestep Methods 27
XIV CONTENTS 2.6 Implicit Runge-Kutta Methods 55 Second order method Third order method Fourth order method High order implicit Runge-Kutta methods 2.7 Obrechkoff Methods 61 Second order methods Third order methods Fourth order method 2.8 Systems of Differential Equations 67 Taylor series method Runge-Kutta methods Stability analysis Stiff system of differential equations 2.9 Higher Order Differential Equations 73 Runge-Kutta methods Stability analysis 2.10 Adaptive Numerical Methods 81 Runge-Kutta-Treanor method Runge-Kutta-Liniger-Willoughby method Runge-Kutta-Nystrom-Treanor method Bibliographical note Problems Chapter 3. Multistep Methods 93 3.1 Introduction 93 3.2 Explicit Multistep Methods 94 Adams-Bashforth formulas 0=0) Nystrom formulas 0=1) Formulas for, j= 0, 1, 3, 5 Results from computation for predictor methods 3.3 Implicit Multistep Methods 102 Adams-Moulton formulas 0=0) Milne-Simpson formulas 0= 1) 3.4 Multistep Methods based on Differentiation 105 3.5 General Linear Multistep Methods 106 Determination of a and bi Estimate of truncation error Stability and convergence Other stability results Propagated error estimates 3.6 Predictor-Corrector Methods 126 Use of implicit multistep methods P(EC) m E scheme Results from computation for Adams P-C methods Modified predictor-corrector methods 3.7 Hybrid Methods 140 One step hybrid methods Two step hybrid methods Implementation of hybrid predictor-corrector methods
CONTENTS XV 3.8 Higher Order Differential Equations 147 Hybrid methods ObrechkofF methods Adaptive numerical methods Results from computation 3.9 Non-uniform Step Methods 160 Adams-Bashforth methods Adams-Moulton methods Results from computation Bibliographical note Problems Chapter 4. Difference Methods for Boundary Value Problems in Ordinary Differential Equations 173 4.1 Introduction 173 4.2 Approximate Methods 174 Shooting methods Difference methods Difference approximation to derivatives 4.3 Nonlinear Boundary Value Problem .1’ = fix, y) 180 Difference scheme based on quadrature formulas Second order linear boundary value problems Solution of tridiagonal system Mixed boundary conditions Boundary condition at infinity High order methods 4.4 Nonlinear Boundary Value Problem y =f{x,y,y ) 200 Difference schemes Compact implicit difference schemes Difference schemes based on cubic spline function Second order linear differential equation with significant first derivative 4.5 Convergence of Difference Schemes 213 4.6 Nonlinear Boundary Value Problem y ( ° =ƒ(*, y) 218 Difference schemes Fourth order linear boundary value problem Solution of five-band system 4.7 Linear Eigenvalue Problems 225 Eigenvalues and eigenvectors The iteration method Convergence analysis 4.8 Results from Computation 232 4.9 Nonuniform Grid Methods for the Second Order Boundary Value Problems 235 Nonlinear boundary value problems y =f(x,y) Nonlinear boundary value problems v =f(x, y, y )
xvi CONTENTS Results from computation Bibliographical note Problems Chapter 5. Difference Methods for Parabolic Partial Differential Equations 251 5.1 Introduction 251 5.2 Difference Methods 254 5.3 Difference Schemes for Equations in One Space Dimension with Constant Coefficients 258 Two level explicit difference schemes Multilevel explicit difference schemes Explicit difference schemes for the diffusion convection equation Two level implicit difference schemes Multilevel implicit difference schemes Implicit difference schemes for the diffusion convection equation 5.4 Implementation of Difference Schemes 277 The initial value problem The initial Dirichlet boundary value problem The initial mixed boundary value problem Results from computation 5.5 Stability Analysis and Convergence of Difference Schemes 288 Matrix stability analysis Convergence of difference schemes 5.6 Difference Schemes for Equations in Two Space Variables with Constant Coefficients 296 Explicit difference schemes Implicit difference schemes Alternating direction implicit (ADI) methods 5.7 ADI Methods for Equations in Two Space Variables with a Mixed Derivative 309 Two level implicit difference schemes Three level methods Results from computation 5.8 ADI Methods for Equations in Three Space Variables with Constant Coefficients 316 5.9 Difference Schemes for Equations with Variable Coefficients 321 One space dimension Two space dimensions Three space dimensions Stability analysis ADI formulas Results from computation 5.10 Difference Schemes for Fourth Order Equations 335 Direct procedure
CONTENTS XVII The Richtmyer procedure Results from computation 5.11 Nonlinear Parabolic Equations 349 Iteration methods 5.12 Difference Schemes for Equations with Cylindrical Symmetry 359 Implicit two level schemes Approximation at the boundary Two space variables Results from computation Bibliographical note Problems Chapter 6. Difference Methods for Hyperbolic Partial Differential Equations 380 6.1 Introduction 380 6.2 Difference Schemes for Hyperbolic Equations in One Space Variable with Constant Coefficients 380 Explicit difference schemes Implicit difference schemes Results from computation 6.3 Difference Schemes for Equations in Two Space Variables with Constant Coefficients 389 Explicit difference schemes Implicit difference schemes ADI methods Results from computation 6.4 Difference Schemes for Equations in Three Space Variables with Constant Coefficients 398 6.5 Difference Schemes for Equations with Variable Coefficients 400 One space dimension Two space dimensions Results from computation 6.6 Locally One Dimensional (LOD) Methods 405 Two space dimensions Three space dimensions Results from computation 6.7 Difference Schemes for System of Equations in One Space Variable 407 First order hyperbolic scalar equation System of equations Systems in conservation form Stability analysis 6.8 Implementation of Difference Schemes 419 Initial boundary value problem Results from computation
xviii Chapter 7. Chapter 8. CONTENTS 6.9 Difference Schemes for System of Equations in Two Space Variables 427 Stability analysis Systems of conservation laws in two space dimensions Results from computation Bibliographical note Problems Difference Methods for Elliptic Partial Differential Equations 448 7.1 Introduction 448 7.2 Difference Schemes 448 Difference approximation to p 2 Difference approximation to p 4 7.3 Dirichlet Problem 458 1A Iterative Methods 461 Jacobi method Gauss-Seidel method Successive over-relaxation (SOR) method Richardson method Results from computation 7.5 Alternating Direction Method 476 7.6 Neumann Problem 484 Derivative condition at the curved boundary 7.7 Third Boundary Value Problem 487 7.8 Diffusion Convection Equation 489 7.9 Axially Symmetric Equation 493 7.10 Biharmonic Equation 496 Bibliographical note Problems Finite Element Methods 513 8.1 Introduction 513 8.2 Weighted Residual Methods 513 Least square method Partition method Galerkin method Moment method Collocation method 8.3 Variational Methods 522 Ritz method 8.4 Finite Elements 528 Line segment element Triangular element Rectangular element Quadrilateral element Tetrahedron element Hexahedron element
CONTENTS XIX Curved boundary element Numerical integration over finite elements 8.5 Finite Element Methods 559 Ritz finite element method Least square finite element method Galerkin finite element method Convergence analysis 8.6 Boundary Value Problems in Ordinary Differential Equations 563 Assembly of element equations Mixed boundary conditions Galerkin method 8.7 Boundary Value Problem in Partial Differential Equations 575 Assembly of element equations Mixed boundary conditions Boundary points Galerkin method 8.8 Nonlinear Differential Equations 606 8.9 initial Value Problems in Ordinary Differential Equations 609 First order initial value problems Second order initial value problems 8.10 Initial Boundary Value Problems 615 Parabolic equation First order hyperbolic equation Second order hyperbolic equation Bibliographical note Problems Bibliography 645 Answers and Hints to the Problems 660 Index 695
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002114539 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:35Z |
| institution | BVB |
| isbn | 0852264321 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001386874 |
| oclc_num | 46072913 |
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| owner | DE-91G DE-BY-TUM DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-706 |
| physical | XIX, 698 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Wiley Eastern |
| record_format | marc |
| spelling | Jain, Mahinder K. Verfasser aut Numerical solution of differential equations 2. ed. New Delhi u.a. Wiley Eastern 1984 XIX, 698 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentialgleichung - Numerische Mathematik idsbb Numerische Mathematik - Differentialgleichung idsbb Differential equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001386874&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jain, Mahinder K. Numerical solution of differential equations Differentialgleichung - Numerische Mathematik idsbb Numerische Mathematik - Differentialgleichung idsbb Differential equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4012249-9 |
| title | Numerical solution of differential equations |
| title_auth | Numerical solution of differential equations |
| title_exact_search | Numerical solution of differential equations |
| title_full | Numerical solution of differential equations |
| title_fullStr | Numerical solution of differential equations |
| title_full_unstemmed | Numerical solution of differential equations |
| title_short | Numerical solution of differential equations |
| title_sort | numerical solution of differential equations |
| topic | Differentialgleichung - Numerische Mathematik idsbb Numerische Mathematik - Differentialgleichung idsbb Differential equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung - Numerische Mathematik Numerische Mathematik - Differentialgleichung Differential equations Numerical solutions Numerisches Verfahren Differentialgleichung |
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