Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

doi:10.1007/s11464-009-0001-0

Front Math Chin

2009, Vol. 4

Issue (1) : 3-22 https://doi.org/10.1007/s11464-009-0001-0

SURVEY ARTICLE

Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

Hermann BRUNNER^1,2(

)

1. Department of Mathematics and Statistics, Memorial University of Newfoundland,St. John’s, NL A1C 5S7, Canada; 2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

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Abstract

The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with θ(t) = qt (0 < q< 1, t ≥ 0) being an important special case), and (ii) to point, by means of a list of open problems, to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.

Keywords Volterra functional integral and integro-differential equation vanishing delay pantograph equation collocation solution optimal order of superconvergence

Corresponding Author(s): BRUNNER Hermann,Email:hermann@math.mun.ca, hbrunner@math.hkbu.edu.hk

Issue Date: 05 March 2009

Cite this article:

Hermann BRUNNER. Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays[J]. Front Math Chin, 2009, 4(1): 3-22.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0001-0
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I1/3

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