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

Authors

  • Muhammad Naveed Akhtar Department of Computer and Information Science (DCIS), Pakistan Institute of Engineering & Applied Sciences (PIEAS)
  • Muhammad Hanif Durad Department of Computer and Information Science (DCIS), Pakistan Institute of Engineering & Applied Sciences (PIEAS)
  • Anila Usman Department of Computer and Information Science (DCIS), Pakistan Institute of Engineering & Applied Sciences (PIEAS)
  • Irfan ul Haq Department of Computer and Information Science (DCIS), Pakistan Institute of Engineering & Applied Sciences (PIEAS)

DOI:

https://doi.org/10.21015/vtm.v8i1.579

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.

References

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Published

2019-12-31

How to Cite

Akhtar, M. N., Durad, M. H., Usman, A., & Haq, I. ul. (2019). Unified Computational Analysis of Conventional Numerical Methods for Time Dependant Heat Equation. VFAST Transactions on Mathematics, 7(1), 39–48. https://doi.org/10.21015/vtm.v8i1.579

Issue

Vol. 7 No. 1 (2019): January-December

Section

Articles

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