Semi analytical iterative method for solving Painlev´e Equation I / Mat Salim Selamat ... [et al.]

The Painlev´e equation I is one of the six Painlev´e equations which are second order nonlinear ordinary differential equations. The generic solutions of the Painlev´e equations are transcendental in the sense that they cannot be expressed in terms of known functions that is difficult to solve analytically (Clarkson, 2003). Therefore, some numerical methods are recommended to solve this problems. In this study, the Painlev´e equation I will be numerically simulated by a semi analytical iterative method (SAIM) (Temimi and Ansari, 2011) and the results will be compared with the fourth-order classical Runge-Kutta method (RK4) and other references. The calculation algorithm has been coded through MAPLE 2020 software.