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A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel

A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel
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Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 424–446

Abstract

This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation with a weakly singular kernel. The solution of this equation, even for analytic data, is not smooth on the entire interval of integration. The Jacobi collocation discretization is proposed for the given equation. A rigorous analysis of error bound is also provided which theoretically justifies that both the error of approximate solution and the error of approximate derivative of the solution decay exponentially in $L^∞$ norm and weighted $L^2$ norm. Numerical results are presented to demonstrate the effectiveness of the spectral method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.1125nm

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 424–446

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Neutral Volterra integro-differential equation weakly singular kernel Jacobi collocation discretization convergence analysis.

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