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Convergence of iterative methods for solving Painlevé equation. (English) Zbl 1204.65096
Summary: A Painlevé equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), homotopy perturbation method (HPM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.
65L99 Numerical methods for ordinary differential equations
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