Difference Equations from Differential Equations

  • Wilbert James Lick

Part of the Lecture Notes in Engineering book series (LNENG, volume 41)

Table of contents

  1. Front Matter
    Pages N1-X
  2. Wilbert James Lick
    Pages 1-72
  3. Wilbert James Lick
    Pages 73-126
  4. Wilbert James Lick
    Pages 127-191
  5. Wilbert James Lick
    Pages 192-218
  6. Wilbert James Lick
    Pages 219-272
  7. Back Matter
    Pages 273-287

About this book

Introduction

In computational mechanics, the first and quite often the most difficult part of a problem is the correct formulation of the problem. This is usually done in terms of differential equations. Once this formulation is accomplished, the translation of the governing differential equations into accurate, stable, and physically realistic difference equations can be a formidable task. By comparison, the numerical evaluation of these difference equations in order to obtain a solution is usually much simpler. The present notes are primarily concerned with the second task, that of deriving accurate, stable, and physically realistic difference equations from the governing differential equations. Procedures for the numerical evaluation of these difference equations are also presented. In later applications, the physical formulation of the problem and the properties of the numerical solution, especially as they are related to the numerical approximations inherent in the solution, are discussed. There are numerous ways to form difference equations from differential equations.

Keywords

Algebra algorithm algorithms hyperbolic equation linear algebra numerical methods partial differential equation

Authors and affiliations

  • Wilbert James Lick
    • 1
  1. 1.Dept. of Mechanical and Environmental EngineeringUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-83701-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50739-0
  • Online ISBN 978-3-642-83701-2
  • Series Print ISSN 0176-5035
  • About this book