Unified Computational Analysis of Conventional Numerical Methods for Time Dependant Heat Equation

Muhammad Naveed Akhtar, Muhammad Hanif Durad, Anila Usman, Irfan ul Haq

Abstract


The objective of this paper is to perform a unified error and computation time analysis of conventional numerical methods for solving the heat equation. The numerical techniques employed include Forward Difference, Backward Difference, Crank Nicolson, Alternate Directions Scheme, and DuFort-Frankel methods for the time-dependent heat equation. The heat equation has been implemented to 1-D, 2-D, and 3-D problems, both for the Neumann and Dirichlet boundary conditions. On basis of experimental results, theoretical justifications have been provided regarding the performance of each method.

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DOI: http://dx.doi.org/10.21015/vtm.v8i1.579

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