Asymptotic Error Expansion for the Nystrom Method of Nonlinear Volterra Integral Equation of the Second Kind
Year: 1994
Author: Guo-Qiang Han
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 31–35
Abstract
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper, we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approximate solution admits an asymptotic error expansion in even powers of the step-size $h$, beginning with a term in $h^2$. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1994-JCM-10223
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 31–35
Published online: 1994-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 5