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)
	© 2015 by IJMTT Journal
	Volume-27 Number-1
	Year of Publication : 2015
	Authors : S. Kaunanithi, S. Chakravarthy, S. Sekar
	10.14445/22315373/IJMTT-V27P505

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). V27(1):25-30 November 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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.

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