Numeric-Analytic Form of the Adomian Decomposition Method for Two-Point Boundary Value Problems in Nonlinear Mechanics
Publication: Journal of Engineering Mechanics
Volume 133, Issue 10
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.
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Acknowledgments
D. Roy would like to express his appreciation for the numerical work done by Mr. Anubhab Roy, a summer research trainee, funded by the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 10 • October 2007
Pages: 1124 - 1133
Copyright
© 2007 ASCE.
History
Received: Apr 24, 2006
Accepted: Mar 7, 2007
Published online: Oct 1, 2007
Published in print: Oct 2007
Notes
Note. Associate Editor: Arif Masud
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