Solving the first Painleve equation using the Sinc-Galerkin method

Abstract

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