A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the method of lines (MOL), a well-established numerical procedure for all major classes of PDEs in which the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and thus 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 as related to the associated equations of the PDE model.
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
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'The presented book is very interesting not only for students in applied mathematics, physics and engineering, but also for their teachers and can act as an effective and useful motivation in their work.' Zentralblatt MATH
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Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
| Preface |
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ix | |
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An Introduction to the Method of Lines |
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1 | (17) |
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A One-Dimensional, Linear Partial Differential Equation |
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18 | (18) |
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Green's Function Analysis |
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36 | (34) |
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Two Nonlinear, Variable-Coeffcient, Inhomogeneous Partial Differential Equations |
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70 | (20) |
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Euler, Navier Stokes, and Burgers Equations |
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90 | (24) |
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The Cubic Schrodinger Equation |
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114 | (27) |
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The Korteweg-deVries Equation |
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141 | (30) |
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171 | (32) |
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203 | (26) |
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Elliptic Partial Differential Equations: Laplace's Equation |
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229 | (32) |
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Three-Dimensional Partial Differential Equation |
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261 | (30) |
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Partial Differential Equation with a Mixed Partial Derivative |
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291 | (15) |
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Simultaneous, Nonlinear, Two-Dimensional Partial Differential Equations in Cylindrical Coordinates |
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306 | (36) |
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Diffusion Equation in Spherical Coordinates |
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342 | (39) |
| Appendix 1 Partial Differential Equations from Conservation Principles: The Anisotropic Diffusion Equation |
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381 | (17) |
| Appendix 2 Order Conditions for Finite-Difference Approximations |
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398 | (16) |
| Appendix 3 Analytical Solution of Nonlinear, Traveling Wave Partial Differential Equations |
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414 | (6) |
| Appendix 4 Implementation of Time-Varying Boundary Conditions |
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420 | (21) |
| Appendix 5 The Differentiation in Space Subroutines Library |
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441 | (4) |
| Appendix 6 Animating Simulation Results |
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445 | (24) |
| Index |
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469 | |
William E. Schiesser is the Emeritus R. L. McCann Professor of Chemical Engineering and a Professor of Mathematics at Lehigh University. He is also a visiting professor at the University of Pennsylvania and the co-author of the Cambridge book Computational Transport Phenomena. Graham W. Griffiths is a visiting professor in the School of Engineering and Mathematical Sciences of City University, London, having previously been a senior visiting Fellow. He is also a founder of Special Analysis and Simulation Technology Ltd and has worked extensively in, and researched into, the field of dynamic simulation of chemical processes.
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