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Hermite-type method for Volterra integral equation with certain weakly singular kernel. (English) Zbl 0841.65127

Authors’ abstract: We discuss the Hermite-type collocation method for the solution of Volterra integral equations with weakly singular kernel. The constructed approximation is a cubic spline in the community class \(C^1\). We prove that this method is convergent with order of four.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)