A new approach based on generalised multiquadric and compactly supported radial basis functions for solving two-dimensional Volterra-Fredholm integral equations

This article describes a numerical scheme to solve two-dimensional nonlinear Volterra-Fredholm integral equations (IEs). The method estimates the solution by compactly supported radial basis functions and compared with the approximation of the solution by generalised multiquadric radial basis function with the optimal strategy for the exponent beta. Integrals appearing in the procedure of the solution are approximated using shifted Legendre-Gauss-Lobatto nodes and weights. The method is mathematically simple and truly meshless. It can be used for high-dimensional problems because it does not require any cell structures. Finally, numerical experiments are given to show and test the applicability of the presented approach and confirm the theoretical analysis.