9. The Finite Difference Method

  1. Richard A. Bernatz

Published Online: 18 AUG 2010

DOI: 10.1002/9780470651384.ch9

Fourier Series and Numerical Methods for Partial Differential Equations

Fourier Series and Numerical Methods for Partial Differential Equations

How to Cite

Bernatz, R. A. (2010) The Finite Difference Method, in Fourier Series and Numerical Methods for Partial Differential Equations, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470651384.ch9

Publication History

  1. Published Online: 18 AUG 2010
  2. Published Print: 6 JUL 2010

ISBN Information

Print ISBN: 9780470617960

Online ISBN: 9780470651384

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Keywords:

  • finite difference method;
  • heat equation;
  • Crank-Nicholson method;
  • error and stability;
  • wave equation

Summary

This chapter contains sections titled:

  • Discretization

  • Finite Difference Formulas

  • ID Heat Equation

  • Crank-Nicolson Method

  • Error and Stability

  • Convergence in Practice

  • ID Wave Equation

  • 2D Heat Equation in Cartesian Coordinates

  • Two-Dimensional Wave Equation

  • 2D Heat Equation in Polar Coordinates