Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels

Abstract

We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experiments are given, which confirm our theoretical results.