A Nyström interpolant for some weakly singular linear Volterra integral equations

We consider a second kind weakly singular nonlinear Volterra-Hammerstein integral equation defined by a compact operator and derive a Nystrom type interpolant of the solution based on Gauss-Radau nodes. We prove the convergence of the interpolant and derive convergence estimates. For equations with nonlinearity of algebraic kind, we improve the rate of convergence by using a smoothing transformation. Some numerical examples are given.

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