Solving Partial Differential Equation Applications with PDE2D

Title:

Personal Author:

Sewell, Granville, author

Physical Description:

viii, 209 pages : illustrations ; 24 cm.

ISBN:

9781119507932

Subject Term:

Differential equations, Partial -- Numerical solutions -- Computer programs

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010369571	QA377 S49 2018	Open Access Book	Book	Searching... Unknown

Summary

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 www.pde2d.com 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 www.pde2d.com

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.

Author Notes

Granville Sewell, PhD, is Professor in the Mathematics department at the University of Texas-El Paso, El Paso, TX. Dr. Sewell is the author of The Numerical Solution of Ordinary and Partial Differential Equations, Second Edition, and Computational Methods of Linear Algebra, Second Edition, both published by Wiley.

Preface	p. vii
1 Introduction to PDE2D	p. 1
1.1 The Collocation and Galerkin Finite Element Methods	p. 1
1.2 The PDE2D User Interfaces	p. 7
1.3 Accuracy	p. 11
1.4 Computer Time and Memory	p. 13
1.5 Programming Hints	p. 17
1 The Damped Spring and Pendulum Problems	p. 21
1.1 Derivation of the Damped Spring and Pendulum Equations	p. 21
1.2 Damped Spring and Pendulum Examples	p. 23
1.3 Problems	p. 24
2 Beam and Plate Bending	p. 31
2.1 Derivation of Beam Bending Equation	p. 31
2.2 Derivation of Plate Bending Equation	p. 32
2.3 Beam and Plate Examples	p. 33
2.4 Problems	p. 34
3 Diffusion and Heat Conduction	p. 39
3.1 Derivation of Diffusion Equation	p. 39
3.2 Diffusion and Heat Conduction Examples	p. 40
3.3 Problems	p. 51
4 Pricing Options	p. 61
4.1 Derivation of Black-Scholes Equation	p. 61
4.2 Option Pricing Examples	p. 65
4.3 Problems	p. 70
5 Elasticity	p. 75
5.1 Derivation of Elasticity Equations	p. 75
5.2 Elasticity Examples	p. 77
5.3 Problems	p. 81
6 Incompressible Fluid Flow	p. 95
6.1 Derivation of Navier-Stokes Equations	p. 95
6.2 Stream Function and Penalty Method Approaches	p. 97
6.3 Fluid Flow Examples	p. 97
6.4 Problems	p. 105
7 The Schrödinger and Other Eigenvalue Equations	p. 119
7.1 The Schrödinger Equation	p. 119
7.2 Schrödinger and Maxwell Equations Examples	p. 119
7.3 Problems	p. 126
8 Minimal Surface and Membrane Wave Equations	p. 137
8.1 Derivation of Minimal Surface Equation	p. 137
8.2 Derivation of Membrane Wave Equation	p. 138
8.3 Examples	p. 140
8.4 Problems	p. 142
9 The KPI Wave Equation	p. 149
9.1 A Difficult Nonlinear Problem	p. 149
9.2 Numerical Results	p. 155
Appendix A Formulas from Multivariate Calculus	p. 161
Appendix B Algorithms Used by PDE2D	p. 163
Appendix C Equations Solved by PDE2D	p. 183
Appendix D Problem 5.7 Local Solvers	p. 193
References	p. 205
Index	p. 207

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Summary

Summary

Author Notes

Table of Contents