Document Type : Research Paper
Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
In this article, using the properties of the rationalized Haar (RH) wavelets and the matrix operator, a method is presented for calculating the numerical approximation of the first Painlev'e equations solution. Also, an upper bound of the error is given and by applying the Banach fixed point theorem the convergence analysis of the method is stated. Furthermore, an algorithm to solve the first Painlev'e equation is proposed. Finally, the reported results are compared with some other methods to show the effectiveness of the proposed approach.