Gaussian radial basis functions and spectral collocation methods for the solution of two-dimensional singular system of Volterraintegral equations

Gaussian radial basis functions and spectral collocation methods for the solution of two-dimensional singular system of Volterraintegral equations

The existence and uniqueness solution of singular system of the Volterra integral equations (TIAEs) is investigated by extending the notions of the tractability index for these systems. Two numerical techniques based on the radial basis functions and the spectral collocation method are presented for the solution of TIAEs. Similarly to spectral methods, the rate of convergence of the numerical methods based on the radial basis functions are exponen- tial. Then these two proposed numerical methods is compared and the performance of the numerical schemes are illustrated by means of some test problems.