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A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact...
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