Numeric-Analytic Form of the Adomian Decomposition Method for Two-Point Boundary Value Problems in Nonlinear Mechanics

Ghosh, S and Roy, D (2007) Numeric-Analytic Form of the Adomian Decomposition Method for Two-Point Boundary Value Problems in Nonlinear Mechanics. In: Journal of Engineering Mechanics, 133 (10). pp. 1124-1133.

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Abstract

A new numeric-analytic technique is developed for two-point nonlinear boundary-value problems (BVPs) of engineering interest. The analytic part of the method is based on a conventional Adomian decomposition method (ADM). However, given a discretization of the one-dimensional domain, the present algorithm applies the ADM, repetitively over successive intervals and exploits a shooting algorithm to solve the BVPs. Apart from a very high rate of convergence as the discretization is made finer, yet another significant advantage of the method is that it provides the solution in a piecewise functional form and one can finally arrive at a continuous form of the global solution. The procedure is used to study planar, large-deflection (Elastica) problem of a cantilever beam subjected to a transverse, concentrated load, at its free end. Moreover the elastoplastic behavior of a cantilever is also studied. Comparisons with exact solutions as well as with results via a few other competing algorithms demonstrate the remarkable accuracy of the proposed method.

Item Type:	Journal Article
Publication:	Journal of Engineering Mechanics
Publisher:	American Society of Civil Engineers
Additional Information:	Copyright of this article belongs to American Society of Civil Engineers.
Keywords:	Decomposition;Numerical analysis;Algorithms;Differential equations.
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	01 Aug 2008
Last Modified:	19 Sep 2010 04:48
URI:	http://eprints.iisc.ac.in/id/eprint/15414

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