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Finite Difference Methods for Parabolic PDEs

  • David F. GriffithsEmail author
  • John W. Dold
  • David J. Silvester
Chapter
  • 4.8k Downloads
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

This self-contained chapter focuses on finite difference approximation of parabolic boundary value problems. Standard explicit and implicit time-stepping schemes are introduced and the quality of resulting numerical approximations is assessed using maximum principles as well as the classical Von Neumann stability framework. The development of method-of-lines software is discussed at the end of the chapter.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David F. Griffiths
    • 1
    Email author
  • John W. Dold
    • 2
  • David J. Silvester
    • 2
  1. 1.University of DundeeFifeUK
  2. 2.School of MathematicsThe University of ManchesterManchesterUK

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