The numerical solution of nonlinear two-dimensional Volterra–Fredholm integral equations of the second kind based on the radial basis functions approximation with error analysis

In this paper, we present a numerical method for solving two-dimensional nonlinear Volterra–Fredholm integral equations of the second kind. The method approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data. The proposed method is meshless, since it does not require any background mesh or domain elements. Error analysis of this method is also investigated. Numerical examples which compare the proposed method with 2D-TFs method [4] approve its supremacy in terms of accuracy and computational cost. Using various RBFs we have concluded that MQ-RBF is the best choice for the proposed method.