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Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs. (English) Zbl 1217.81054
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:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q15 Perturbation theories for operators and differential equations in quantum theory
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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