Numerical Solution of Linear Volterra Integral Equations Using Non-Uniform Haar Wavelets

Abstract

In this paper, we presented a numerical method for solving linear Volterra integral equations (LVIE) which is based on the non-uniform Haar wavelets. By applying this method, the LVIE is reduced to a linear system of algebraic equations which can be solved by direct method. The min advantage of using non-uniform Haar wavelets is that the time of calculation can be adjusted arbitrarily. Also, we presented the error analysis of the proposed method. Furthermore, two examples are included for the demonstrating the convenient capabilities of the new method.