Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: An hp-version collocation approach

Abstract

This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of this nonlinear Volterra integral equations is studied completely. An hp-version collocation method in conjunction with Jacobi polynomials is introduced so as an appropriate numerical solution to be found. We analyze it properly and find an error estimation in L2-norm. The efficiency of the method is illustrated by some numerical experiments.