An aftertreatment technique for improving the accuracy of Adomian’s decomposition method. (English) Zbl 1005.34006

Summary: Adomian’s decomposition method (ADM) is a nonnumerical method that can be adapted for solving nonlinear ordinary differential equations. Here, the principle of the decomposition method is described, and its advantages as well as drawbacks are discussed. Then an aftertreatment technique (AT) is proposed that yields an analytic approximate solution with fast convergence rate and high accuracy through the application of Padé approximation to the series solution derived from ADM. Some concrete examples are studied to show with numerical results how the AT works efficiently.


34A45 Theoretical approximation of solutions to ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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