Abstract:

The authors proposed a collocation method for solving a class of Volterra integral equations with weakly singular kernel. Firstly, we showed the existence and uniqueness of the solution by the contraction mapping theorem, and then constructed the collocation scheme for this kind of equations together with the error analysis. Finally, the numerical experiments verified our theoretical results. This numerical method is useful for general nonlinear Volterra integral equations.

Key words: weakly singular kernel, Volterra integral equation, collocation method