Wavelet solutions of the second Painleve equation

Document Type : Regular Paper


Department of Mathematics, Faculty of Basic Sciences, Shiraz University of Technology, Modarres Blvd. P.O. Box, 71555-313, Shiraz, Iran


Dynamically adaptive numerical methods have been developed to find solutions for differential equations. The
subject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions for
differential 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.