Wavelet solutions of the second Painleve equation

Abstract

Dynamically adaptive numerical methods have been developed to find solutions for differential equations. Thesubject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions fordifferential equations. Wavelets have the ability to show functions at different levels of resolution. In this paper, a numerical method is proposed for solving the second Painleve equation based on the Legendre wavelet. The solutions of this method are compared with the analytic continuation and Adomian Decomposition methods and the ability of the Legendre wavelet method is demonstrated.