The Numerical Solution of Ordinary and Partial Differential Equations

Granville Sewell

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483259147
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.

Table of contents

• Front Cover
• The Numerical Solution of Ordinary and Partial Differential Equations
• Copyright Page
• Table of Contents
• Preface
• Chapter 0. Direct Solution of Linear Systems
• Chapter 1. Initial Value Ordinary Differential Equations
• Chapter 2. The Initial Value Diffusion Problem
• Chapter 3. The Initial Value Transport and Wave Problems
• Chapter 4. Boundary Value Problems
• Chapter 5. The Finite Element Method
• Appendix 1: The Fourier Stability Method
• Appendix 2: Parallel Algorithms
• References
• Index