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01-03-2019

Analysis of collocation methods for nonlinear Volterra integral equations of the third kind

Authors: Huiming Song, Zhanwen Yang, Hermann Brunner

Published in: Calcolo | Issue 1/2019

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Abstract

We study the approximation of solutions of a class of nonlinear Volterra integral equations (VIEs) of the third kind by using collocation in certain piecewise polynomial spaces. If the underlying Volterra integral operator is not compact, the solvability of the collocation equations is generally guaranteed only if special (so-called modified graded) meshes are employed. It is then shown that for sufficiently regular data the collocation solutions converge to the analytical solution with the same optimal order as for VIEs with compact operators. Numerical examples are given to verify the theoretically predicted orders of convergence.

previous article Finite element discretization of local minimization schemes for rate-independent evolutions

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Title: Analysis of collocation methods for nonlinear Volterra integral equations of the third kind
Authors: Huiming Song
Zhanwen Yang
Hermann Brunner
Publication date: 01-03-2019
Publisher: Springer International Publishing
Published in: Calcolo / Issue 1/2019
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-019-0304-9

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Analysis of collocation methods for nonlinear Volterra integral equations of the third kind

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