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Spectral methods for weakly singular Volterra integral equations with smooth solutions. (English) Zbl 1186.65161

The authors investigate a spectral Jacobi-collocation approximation for finding the solution of a linear Volterra integral equation of the second kind with weakly singular kernel and a sufficiently smooth condition by using the infinity norm and the norm on a weighted Sobolev space based on a paper of B. Guo and L. Wang [J. Approximation Theory 128, No. 1, 1–41 (2004; Zbl 1057.41003)].

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)

Citations:

Zbl 1057.41003
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Full Text: DOI

References:

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