Abstract

We present a new modified version of the Adomian decomposition method for computing the series solutions of the nonlinear ordinary differential equations (ODEs). The recently proposed Adomian matrix algorithm is used in this method to compute the Adomian polynomials for scalar-valued nonlinear polynomial functions, which allows us to get the series solution of the ODEs numerically and makes it much faster than symbolic computation. This method can test the convergence of the series solution of the ODE by calculating the global squared residual error of the solution. Several types of nonlinear ODEs, such as Abel equation, De Boer-Ludford equation, Van der Pol equation, Painleve-Ince equation, and Falkner-Skan equation, are solved using this method to illustrate its performance and effectiveness in delivering solutions.

Keywords and Phrases

ODE, series solution, convergence, Adomian polynomials.

A.M.S. subject classification

34-XX, 34-04, 34A25, 40A05.

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