Abstract
In this paper, we introduce and analyse Nyström-quasilinearization method for the numerical solution of nonlinear weakly singular Fredholm integral equations of the second kind. Under some mild conditions on the equation, applying quasilinearization technique gives a sequence of linear equations with low smooth solutions quadratically convergent to the unique solution of the nonlinear equation. By analysing the behaviour of the solutions near the boundaries and choosing appropriate smoothing transformation, we approximate the solution of the linear equation by Nyström method. Error analysis of the scheme confirms the improvement of the convergence order in comparison with the case without smoothing transformation. The numerical experiments are in agreement with the theoretical results and show the efficiency of the presented method in comparison with the other methods.
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