Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L^∞ and weighted L² norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.