An Accurate Space–Time Pseudospectral Method for Solving Nonlinear Multi-Dimensional Heat Transfer Problems

Bashar Zogheib, Emran Tohidi

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper, we consider the numerical solution of the nonlinear one- and two-dimensional heat transfer problems subject to the given initial conditions and linear Robin boundary conditions. We propose a pseudospectral scheme in both time and spatial discretizations for these problems. The discretization processes are constructed through the multi-variate interpolation of the desired solutions in terms of Chebyshev Gauss Lobbato collocation points. Operational matrices of differentiation are constructed via the tensor products for speeding up of the proposed numerical algorithms’ implementation. Some test problems are provided and the numerical simulations are illustrated to show the spectral accuracy in both space and time of the suggested scheme.

Original languageEnglish
Article number30
JournalMediterranean Journal of Mathematics
Volume14
Issue number1
DOIs
StatePublished - 1 Feb 2017

Keywords

  • Chebyshev Gauss Lobatto collocation points
  • Nonlinear partial differential equations
  • collocation method
  • multi-dimensional heat transfer problems
  • operational matrix of differentiation
  • spectral approximation

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