Solving linear integro-differential equation with Legendre wavelets

In this article, we use the continuous Legendre wavelets on the interval [0, 1) constructed by [M. Razzaghi and S. Yousefi, The Legendre wavelets operational matrix of integration, International Journal of Systems Science, 32Equation(4) (2001) 495–502.] to solve the linear second kind integro-differential equations and construct the quadrature formulae for the calculation of inner products of any functions, which are required in the approximation for the integro-differential equations. Then we reduce the integro-differential equation to the solution of linear algebraic equations. E-mail: ahadi@khuisf.ac.ir