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

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


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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Heath, Michael T. (2001), Scientific computing. McGraw-Hill,.

Pinchover, Y., & Rubinstein, J. (2005). An introduction to partial differential equations. Cambridge university press.

Romão, E. C., Campos-Silva, J. B., & De Moura, L. F. M. (2009). Error analysis in the numerical solution of 3D convection-diffusion equation by finite difference methods. Revista de Engenharia Térmica, 8(1), 12-17.

Babuška, I., & Szymczak, W. G. (1982). An error analysis for the finite element method applied to convection diffusion problems. Computer Methods in Applied Mechanics and Engineering, 31(1), 19-42.

Ascher, U. M., Ruuth, S. J., & Wetton, B. T. (1995). Implicit-explicit methods for time-dependent partial differential equations. SIAM Journal on Numerical Analysis, 32(3), 797-823.

Lambert, J. D. (1991). Numerical methods for ordinary differential systems: the initial value problem. John Wiley & Sons, Inc..

Zwillinger, D. (1998). Handbook of differential equations (Vol. 1). Gulf Professional Publishing.

Morton, K. W., & Mayers, D. F. (2005). Numerical solution of partial differential equations: an introduction. Cambridge university press.

LeVeque, R. J. (2007). Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Society for Industrial and Applied Mathematics.

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


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