Hybrid Functions Method Based on Radial Basis Functions for Solving Nonlinear Fredholm Integral Equations

A numerical technique based on hybrid of radial basis functions including Guassians (GAs) and Multiquadrics (MQs) is proposed to obtain the solution of nonlinear Fredholm integral equations. Zeros of the shifted Legendre polynomials are used as the collocation points. The integral involved in the formulation of the problems are approximated based on Legendre-Gauss-Lobatto integration rule. Some numerical examples illustrate the accuracy and validity of the proposed method.