ABSTRACT
Volterra integral equations of the first kind arise naturally in various problems. Many problems in mathematical physics, engineering, and integral geometry are often reduced to first-kind Volterra integral equations. A survey of regularization methods for first kind Volterra equations is given by Lamm. This chapter uses the Legendre wavelet to solve Volterra integral equations of the first kind. The aim is to present an efficient numerical method to find a stable solution of Volterra integral equations of the first kind. The chapter commences with an introduction to Legendre wavelets and an approximation of function using Legendre wavelets. It also introduces a local regularization method and presents the numerical method to find an approximate solution to the given problem. The convergence and error analysis is considered and some numerical examples are presented to verify the accuracy of the numerical method.
