A compendium of partial differential equation models : method of lines analysis with Matlab / William E. Schiesser, Graham W. Griffiths.

Includes bibliographical references and index.

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.

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 computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.

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