Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634910 | Applied Mathematics and Computation | 2008 | 25 Pages |
Abstract
Piecewise homotopy perturbation methods are developed for the solution of nonlinear ordinary differential equations. These methods are based on the introduction of an artificial or book-keeping parameter and the expansion of the solution in a power series of this parameter and provide analytical solutions in open intervals which are smooth everywhere. Three piecewise-adaptive homotopy perturbation methods based on the use of either a fixed number of approximants and a variable step size, a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size, are presented and applied to eight nonlinear ordinary differential equations. It is shown that piecewise-adaptive homotopy perturbation methods predict essentially the same solutions as MATLAB's variable-step, variable-order solvers and variable-order transition matrix techniques provided that five-term approximations of the decomposition method are applied to both the displacement and the velocity. It is also shown that piecewise homotopy perturbation techniques that use three-term approximations to both the displacement and the velocity provide essentially the same results as those obtained with a second-order accurate time-linearization technique when the same step is employed in both schemes.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
J.I. Ramos,