Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities.

Filon collocation methods are well known for their good performances in solving the second-kind highly oscillatory Volterra integral equations with weak singularities. As the frequency increases, these methods can provide much more accurate solutions for oscillatory integral equations. This paper is devoted to investigating frequency-related properties of collocation solutions of highly oscillatory Volterra equations with weakly singular kernels. Optimal convergence rates are obtained by analyzing the error equations and studying asymptotic properties of oscillatory integrals involving Bessel functions. Moreover, numerical experiments are conducted to verify the given theoretical results. [ABSTRACT FROM AUTHOR]