Abstract

FILOBELLO-NINO, U. et al. Perturbation Method and Laplace-Padé Approximation as a Novel Tool to Find Approximate Solutions for Troeschs Problem. Nova scientia [online]. 2015, vol.7, n.14, pp.57-73. ISSN 2007-0705.

In this article, Perturbation Method (PM) is employed to obtain an approximate solution for Troesch equation. In addition, we will describe the use of Laplace transform and Padé transformation to deal with the truncated series obtained by the PM method, in order to obtain handy approximations. Finally a table of comparison, between proposed solution, and other solutions reported in the literature: Adomian's Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and exact numerical solution, shows that our solution is the most accurate one (Average Absolute Relative Error 1.705648354x10-8).

Keywords : Troesch Equation; Nonlinear Differential Equation; Perturbation Method; Laplace transform; Padé transformation.

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