Solving Partial Differential Equation Applications with PDE2D

Solving Partial Differential Equation Applications with PDE2D

by Granville Sewell
Released October 2018
Publisher(s): Wiley
ISBN: 9781119507932

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Book description

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.

Table of contents

  1. Cover
  2. Preface
  3. I Introduction to PDE2D
    1. I.1 The Collocation and Galerkin Finite Element Methods
    2. I.2 The PDE2D User Interfaces
    3. I.3 Accuracy
    4. I.4 Computer Time and Memory
    5. I.5 Programming Hints
  4. 1 The Damped Spring and Pendulum Problems
    1. 1.1 Derivation of the Damped Spring and Pendulum Equations
    2. 1.2 Damped Spring and Pendulum Examples
    3. 1.3 Problems
  5. 2 Beam and Plate Bending
    1. 2.1 Derivation of Beam Bending Equation
    2. 2.2 Derivation of Plate Bending Equation
    3. 2.3 Beam and Plate Examples
    4. 2.4 Problems
  6. 3 Diffusion and Heat Conduction
    1. 3.1 Derivation of Diffusion Equation
    2. 3.2 Diffusion and Heat Conduction Examples
    3. 3.3 Problems
  7. 4 Pricing Options
    1. 4.1 Derivation of Black–Scholes Equation
    2. 4.2 Option Pricing Examples
    3. 4.3 Problems
  8. 5 Elasticity
    1. 5.1 Derivation of Elasticity Equations
    2. 5.2 Elasticity Examples
    3. 5.3 Problems
  9. 6 Incompressible Fluid Flow
    1. 6.1 Derivation of Navier–Stokes Equations
    2. 6.2 Stream Function and Penalty Method Approaches
    3. 6.3 Fluid Flow Examples
    4. 6.4 Problems
  10. 7 The Schrödinger and Other Eigenvalue Equations
    1. 7.1 The Schrödinger Equation
    2. 7.2 Schrödinger and Maxwell Equations Examples
    3. 7.3 Problems
  11. 8 Minimal Surface and Membrane Wave Equations
    1. 8.1 Derivation of Minimal Surface Equation
    2. 8.2 Derivation of Membrane Wave Equation
    3. 8.3 Examples
    4. 8.4 Problems
  12. 9 The KPI Wave Equation
    1. 9.1 A Difficult Nonlinear Problem
    2. 9.2 Numerical Results
  13. Appendix A: Formulas from Multivariate Calculus
  14. Appendix B: Algorithms Used by PDE2D
    1. B.1 The Galerkin and Collocation Finite Element Methods
    2. B.2 1D Steady‐state Collocation Problems
    3. B.3 2D Steady‐state Galerkin Problems
    4. B.4 3D Steady‐state Collocation Problems
    5. B.5 Nonrectangular 3D Regions
    6. B.6 Time‐dependent Problems
    7. B.7 Eigenvalue Problems
    8. B.8 The PDE2D Parallel Solvers
  15. Appendix C: Equations Solved by PDE2D
    1. C.1 0D Problems
    2. C.2 1D Problems (Galerkin Method)
    3. C.3 2D Problems (Galerkin Method)
    4. C.4 1D Problems (Collocation Method)
    5. C.5 2D Problems (Collocation Method)
    6. C.6 3D Problems
  16. Appendix D: Problem 5.7 Local Solvers
    1. D.1 DTD3M,DTD3N,DCG (problem57.f)
    2. D.2 DTD3M,DTD3N,PCG,PBAND (problem57d.f)
  17. References
  18. Index
  19. End User License Agreement

Product information

  • Title: Solving Partial Differential Equation Applications with PDE2D
  • Author(s): Granville Sewell
  • Release date: October 2018
  • Publisher(s): Wiley
  • ISBN: 9781119507932