High-order collocation methods for singular Volterra functional equations of neutral type

Authors:
Hermann Brunner
Affiliations:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 8
Cited 1

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Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

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A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels

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Optimal Superconvergence Orders of Iterated Collocation Solutions for Volterra Integral Equations with Vanishing Delays

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Original article: Nonlinear stability of one-leg methods for neutral Volterra delay-integro-differential equations

Mathematics and Computers in Simulation

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Abstract

In the first part of this paper we present a survey of recent results on the attainable order of (super-) convergence of collocation solutions for systems of Volterra functional integro-differential equations with weakly singular kernels k"@a and variable delay functions @q(t)=t-@t(t). Related functional equations and theoretical and computational aspects of collocation methods for their solution are also described. The paper concludes with comments on ongoing and possible future work.