Technique for solving differential equation by extended Legendre wavelets

Based on analyzing the properties of Legendre wavelets, the extended Legendre wavelets, defined on interval (-r, r), is achieved and its properties are considered. According to the translation property of Legendre wavelets, another method for computing operational matrix of integration P is presented through integrating on subintervals. Furthermore a numerical example for solving linear differential equation, subject to certain conditions, demonstrates the validity and applicability of the matrix P.