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Zbl 1217.81054
Hashim, I.; Chowdhury, M.S.H.
Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs. (English)
[J] Phys. Lett., A 372, No. 4, 470-481 (2008). ISSN 0375-9601

Summary: 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 solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
35Q55 NLS-like (nonlinear Schroedinger) equations
81Q15 Perturbation theories for operators and differential equations
65L06 Multistep, Runge-Kutta, and extrapolation methods
81T80 Simulation and numerical modelling of fields

Keywords: homotopy-perturbation method; Runge-Kutta method; system of ODEs

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Zentralblatt MATH Berlin [Germany]