A compendium of partial differential equation models : method of lines analysis with Matlab /

Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Schiesser, W. E.
Otros Autores: Griffiths, Graham W.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 2009.
Temas:
MATLAB.
MATLAB
Differential equations, Partial > Mathematical models.
Équations aux dérivées partielles > Modèles mathématiques.
MATHEMATICS > Differential Equations > Partial.
Partielle Differentialgleichung
Numerisches Verfahren
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Dedication
  • Contents
  • Preface
  • 1 An Introduction to the Method of Lines
  • SOME PDE BASICS
  • INITIAL AND BOUNDARY CONDITIONS
  • TYPES OF PDE SOLUTIONS
  • PDE SUBSCRIPT NOTATION
  • A GENERAL PDE SYSTEM
  • PDE GEOMETRIC CLASSIFICATION
  • ELEMENTS OF THE MOL
  • ODE INTEGRATION WITHIN THE MOL
  • NUMERICAL DIFFUSION AND OSCILLATION
  • DIFFERENTIAL ALGEBRAIC EQUATIONS
  • HIGHER DIMENSIONS AND DIFFERENT COORDINATE SYSTEMS
  • h- AND p-REFINEMENT
  • ORIGIN OF THE NAME 8220;METHOD OF LINES8221;
  • SOURCES OF ODE/DAE INTEGRATORS
  • REFERENCES
  • 2 A One-Dimensional, Linear Partial Differential Equation
  • 3 Greens Function Analysis
  • APPENDIX A
  • A.1. Verification of Eq. (3.4b) as the Solution to Eq. (3.1)
  • A.2. The Function simp
  • REFERENCES
  • 4 Two Nonlinear, Variable-Coefficient, Inhomogeneous Partial Differential Equations
  • REFERENCE
  • 5 Euler, Navier Stokes, and Burgers Equations
  • REFERENCE
  • 6 The Cubic Schr246;dinger Equation
  • APPENDIX A: SOME BACKGROUND TO SCHR214;DINGERS EQUATION
  • A.1. Introduction
  • A.2. A Nonrigorous derivation
  • REFERENCES
  • 7 The KortewegdeVries Equation
  • APPENDIX A
  • A.1. FD Routine uxxx7c
  • APPENDIX B
  • B.1. Jacobian Matrix Routine jpattern_num
  • APPENDIX C
  • C.1. Some Background to the KdV Equation
  • REFERENCES
  • 8 The Linear Wave Equation
  • APPENDIX A
  • A.1. ODE Routines pde_1, pde_2, pde_3
  • REFERENCES
  • 9 Maxwells Equations
  • 10 Elliptic Partial Differential Equations: Laplaces Equation
  • REFERENCES
  • 11 Three-Dimensional Partial Differential Equation
  • 12 Partial Differential Equation with a Mixed Partial Derivative
  • REFERENCE
  • 13 Simultaneous, Nonlinear, Two-Dimensional Partial Differential Equations in Cylindrical Coordinates
  • APPENDIX A
  • A.1. Units Check for Eqs. (13.1)(13.13)
  • REFERENCES
  • 14 Diffusion Equation in Spherical Coordinates
  • REFERENCES
  • APPENDIX 1 Partial Differential Equations from Conservation Principles: The Anisotropic Diffusion Equation
  • REFERENCES
  • APPENDIX 2 Order Conditions for Finite-Difference Approximations
  • APPENDIX 3 Analytical Solution of Nonlinear, Traveling Wave Partial Differential Equations
  • REFERENCES
  • APPENDIX 4 Implementation of Time-Varying Boundary Conditions
  • APPENDIX 5 The Differentiation in Space Subroutines Library
  • FIRST-DERIVATIVE ROUTINES
  • Argument List
  • SECOND-DERIVATIVE ROUTINES
  • Argument List
  • HIGHER-ORDER AND MIXED DERIVATIVES
  • OBTAINING THE DSS LIBRARY
  • APPENDIX 6 Animating Simulation Results
  • GENERAL
  • MATLAB MOVIE
  • BASIC EXAMPLE
  • AVI MOVIES
  • EXAMPLE BURGERS EQUATION MOVIE
  • EXAMPLE SCHR214;DINGER EQUATION MOVIE
  • EXAMPLE KdV EQUATION MOVIE
  • ANIMATED GIF FILES
  • EXAMPLE 3D LAPLACE EQUATION MOVIE
  • EXAMPLE SPHERICAL DIFFUSION EQUATION MOVIE
  • REFERENCES
  • Index.

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