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Solving Partial Differential Equation Applications with PDE2D

  • ID: 4544226
  • Book
  • December 2018
  • 224 Pages
  • John Wiley and Sons Ltd
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Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author 

Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy–to–use, general purpose, and time–tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems.  The equations studied include many time–dependent, steady–state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions.

The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book:

  • Describes a finite–element program, PDE2D, developed by the author over the course of 40 years
  • Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications
  • Offers free access to the Windows version of the PDE2D software through the author s website at [external URL]
  • Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at [external URL]

Written for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.

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Preface

Introduction to PDE2D

1 The Damped Spring and Pendulum Problems

2 Beam and Plate Bending

3 Diffusion and Heat Conduction

4 Pricing Options

5 Elasticity

6 Incompressible Fluid Flow

7 The Schrödinger and Other Eigenvalue Equations

8 Minimal Surface and Membrane Wave Equations

9 The KPI Wave Equation

Appendix A Formulas from Multivariate Calculus 187

Appendix B Algorithms Used By PDE2D 189

Appendix C Equations Solved by PDE2D 211

Appendix D Problem 5.7 Local Solvers 225

References 237

Index 240 

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Granville Sewell
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