Numerical solution of a class of mixed two-dimensional nonlinear Volterra–Fredholm integral equations using multiquadric radial basis functions

Abstract

An efficient numerical method is proposed for solving the mixed nonlinear Volterra–Fredholm two-dimensional integral equations (IEs), using two-dimensional radial basis functions (RBFs). This method is based on interpolation by radial basis functions including multiquadrics (MQs), using Legendre–Gauss–Lobatto nodes and weights. Also a theorem is proved for convergence analysis. Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.