A numerical method based on the radial basis functions for solving nonlinear two-dimensional Volterra integral equations of the second kind on non-rectangular domains

In this investigation, a numerical method for solving nonlinear two-dimensional Volterra integral equations is presented. This method uses radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. Therefore, the method does not need any background mesh or cell structure of the domain. All the integrals that appear in this method are approximated by the composite Gauss-Legendre integration formula. This method transforms the source problem into a system of nonlinear algebraic equations. Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of this technique.

Keywords:

radial basis functions , nonlinear two-dimensional Volterra integral equations , meshless method , non-rectangular domains