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Keywords:

  • finite difference method;
  • integral-differential equation;
  • spectral method;
  • stationary transport equation

Abstract

In this article, a spectral method accompanied by finite difference method has been proposed for solving a boundary value problem that accompanies a stationary transport equation. We also prove that the solution is bounded by a value that depends of the source function. The accuracy and computational efficiency of the proposed method are verified with the help of a numerical example. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012