A Study on unsteady one-dimensional heat flow problem using Rayleigh Ritz, Single-term Walsh series and Leapfrog Method

S. Kaunanithi; S. Chakravarthy; S. Sekar

doi:https://doi.org/10.14445/22315373/IJMTT-V27P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 27 | Number 1 | Year 2015 | Article Id. IJMTT-V27P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V27P505

A Study on unsteady one-dimensional heat flow problem using Rayleigh Ritz, Single-term Walsh series and Leapfrog Method

S. Kaunanithi, S. Chakravarthy, S. Sekar

Abstract

In this article presents a study on interesting unsteady one-dimensional heat flow problem is discussed using Rayleigh Ritz, single-term Walsh series (STWS) method [5] and Leapfrog method. The results (approximate solutions) obtained very accurate using the above said methods are compared with the exact solution of that problem. It is found that the solution obtained using Leapfrog method is closer to the exact solution of the unsteady one-dimensional heat flow problem. The high accuracy and the wide applicability of Leapfrog method approach will be demonstrated with numerical example. Solution graphs for discrete exact solutions are presented in a graphical form to show the efficiency of the Leapfrog method. The results obtained show that Leapfrog method is more useful for solving the unsteady one-dimensional heat flow problem and the solution can be obtained for any length of time.

Keywords

Unsteady one-dimensional heat flow equations, Rayleigh Ritz method, Single-term Walsh series, Leapfrog method.

References

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Citation :

S. Kaunanithi, S. Chakravarthy, S. Sekar, "A Study on unsteady one-dimensional heat flow problem using Rayleigh Ritz, Single-term Walsh series and Leapfrog Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 27, no. 1, pp. 25-30, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V27P505