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arXiv · 1507.01306

Interpolated variational iteration method for initial value problems

Davod Khojasteh Salkuyeh·Ali Tavakoli
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Abstract

In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of the sequence become complicated, and therefore, computing a highly accurate solution would be difficult or even impossible. In this paper, for one-dimensional initial value problems, we propose a new approach which is based on approximating each term of the sequence by a piecewise linear function. Moreover, the convergence of the method is proved. Three illustrative examples are given to show the superiority of the proposed method over the classical variational iteration method.

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Davod Khojasteh Salkuyeh, Ali Tavakoli. 2015-07-05. Interpolated variational iteration method for initial value problems. https://doi.org/10.1016/j.apm.2015.10.037

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