Trigonometric-Interpolation Based Approach for Second-Order Volterra Integro-Differential Equations

Abstract

The trigonometric interpolation has been recently applied to solve a second-order Fredholm integro-differentiable equation (FIDE). It achieves high accuracy with a moderate size of grid points and effectively addresses singularities of kernel functions. In addition, it work well with general boundary conditions and the framework can be generalized to work for FIDEs with a high-order ODE component. In this paper, we apply the same idea to develop an algorithm for the solution of a second-order Volterra integro-differentiable equation (VIDE) with the same advantages as in the study of FIDE. Numerical experiments with various boundary conditions are conducted with decent performances as expected.