Solving the first Painleve equation using the Sinc-Galerkin method

Abstract

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The main goal of this paper is to solve the ?rst Painleve equation using the sinc-Galerkin method. In order to obtain this goal, we ?rst describe brie?y the sinc-Gelrkin method, and then we apply it to the ?rst Painleve equation. At last, the numerical result is shown to demonstrate the power and accuracy of the method.