Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
This paper considers Volterra integral equations of the second kind with highly oscillatory weakly singular Bessel kernels. The aim is to provide numerical approximations to the solution. The authors begin by considering the analytical properties of the problem and of its solution before going on to propose an approximation method. They consider a Filon method and two collocation methods based on piecewise constant and piecewise linear functions. An analysis of errors is provided in each case, illustrated by some numerical examples. The authors conclude by summarising how the methods proposed avoid some of the computational costs and pitfalls of alternative approaches.
scientific article; zbMATH DE number 6150057
scientific article