Interpolation by hybrid Radial Basis Functions for solving nonlinear Volterra-Fredholm-Hammerstein integral equations

Interpolation by radial basis functions technique have grown significantly in recent years due to their ability for solving several problems almost impossible to obtain with standard methods. In this paper, an efficient scheme is given to solve nonlinear one-dimensional Fredholm-Volterra-Hammerstein integral equations, this technique is based on hybrid radial basis functions including the multiquadric, the Gaussian and cubic radial basis functions (RBFs). All integrals appeared in the scheme are approximately computed by the Gauss–Legendre integration formula. The new technique can be used for higher dimensional integral equations and does not increase difficulties in computation due to the easy adaption of radial basis functions. The convergence analysis and the accuracy of the proposed approach are given. Numerical examples clearly show the reliability and efficiency of the method.2000-Mathematics subject classification: 65XX, 65Dxx, 65D12.