Title: Algorithms for solving linear, non-linear differential and differential-difference equations by approximating the solution to polynomials

Authors: Sameh Abdelwahab Nasr Eisa

Addresses: Department of Mathematics, New Mexico Institute of Mining and Technology, 801 Leroy Place, P.O. #3696, Socorro, NM 87801, USA

Abstract: In this paper, a simple methodology for solving initial/boundary value problems for linear/non-linear differential and differential-difference equations is proposed, by approximating the solution to polynomials. The method is based on direct substitution by the assumed polynomials into DEs themselves and then solving system of equations to compute the coefficients of the polynomials. Comparisons of the results are performed with other works published during the last decade through practical examples, which have shown significant progress in the accuracy and the simplicity. This will give the researchers more advantage to use this method especially the engineers.

Keywords: numerical methods; differential equations; differential-difference equations; polynomials; initial value problem; boundary value problem.

DOI: 10.1504/IJCSM.2014.064866

International Journal of Computing Science and Mathematics, 2014 Vol.5 No.3, pp.236 - 251

Received: 19 Jul 2013
Accepted: 31 Jan 2014

Published online: 27 Sep 2014 *

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