Legendre wavelets method for solving Volterra integral equations

Abstract

This thesis presents a numerical solution for linear second-kind Volterra integral equations using the orthogonal Legendre Wavelet Method with collocation. The approach utilizes an operational matrix of integration to transform continuous operators into a linear algebraic system, while existence and uniqueness are proved via Picard iteration. Numerical results demonstrate high accuracy, robust sta bility, and rapid error convergence.