An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 969–994

Abstract

This paper presents an $hp$-version Chebyshev spectral collocation method for nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error bound of the collocation method under the $H$1-norm is established on an arbitrary mesh. Numerical experiments demonstrate the effectiveness of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0104

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 969–994

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Chebyshev spectral collocation method nonlinear Volterra integro-differential equations weakly singular kernels error analysis.

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