Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method

Fatima Hamani, Azedine Rahmoune

Abstract


In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels, we use an appropriate variable transformations to convert the problem set into the unit interval [-1; 1], then the proposed method reduces the main problem to nonlinear system of algebraic equations. The convergence and errors analysis are discussed for both L^{infty} and L^{2}_{w} norms, we confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well known methods to illustrate the eficiency of this method.

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DOI: https://doi.org/10.2478/tmmp-2021-0030