Journal of Computational and Applied Mathematics
Product integration for Volterra integral equations of the second kind with weakly singular kernels
Mathematics of Computation
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Mathematics of Computation
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Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A Nyström interpolant for some weakly singular linear Volterra integral equations
Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
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The approximate solution of a class of Fredholm integral equations with a weakly singular kernel
Journal of Computational and Applied Mathematics
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We consider linear weakly singular Volterra integral equations of the second kind, with kernels of the form k(x, v) = |x - v|-αK(x, v), 0 k(x, v) = log|x - v| K(x - v), K(x, v), being a smooth function. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration. By a transformation of the unknown function we obtain an equation which is still weakly singular, but whose solution is as smooth as we like. This resulting equation is then solved by standard product integration methods.