Spectral method for the diffusion equation with a source term

Document Type : Research Paper


1 Institute of Mathematics, Department of Mathematics, University of Mentouri, Constantine 25000, Algeria

2 Institute of Mathematics, Department of Mathematics, University of Dr. Yahia Fares, Medea, Algeria


The aim of this paper is to investigate the Legendre spectral method for solving the diffusion equation with a source term and mixed initial-boundary value problem in a finite rectangle $\Omega _{2}$, we use some techniques to convert the problem to a system of ordinary differential equations and by an analysis matrical we find a general term defines all ordinary differential equations of this system, we solve this general term we get the desired approximate solution, we also present the error estimate.


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Volume 13, Issue 2
July 2022
Pages 1343-1355
  • Receive Date: 06 January 2020
  • Accept Date: 04 September 2021