Collocation scheme for 2D-VIEs with two constant delays

Abstract

This paper presents a numerical approach for solving linear two-dimensional Volterra integral equations (2D-VIEs) with two distinct time delays using the Taylor collocation method. The method approximates the unknown function by Taylor polynomials and enforces the integral equation at selected collocation points, which can be efficiently solved. A convergence analysis is provided to establish the accuracy and stability of the proposed algorithm. Several numerical examples are included to demonstrate the method's effectiveness in handling problems with multiple delays and smooth kernels. The results show that the Taylor collocation technique achieves high precision at minimal computational cost.