The numerical solution of weakly singular Volterra  functional integro-differential equations  with variable delays

Hermann Brunner

doi:10.3934/cpaa.2006.5.261

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2006, Volume 5, Issue 2: 261-276. Doi: 10.3934/cpaa.2006.5.261

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The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays

Hermann Brunner^1,

1.
Dept. of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7

Received: February 2005

Revised: May 2005

Published: June 2006

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Abstract

We analyze the attainable order of convergence of collocation solutions for linear and nonlinear Volterra functional integro-differential equations of neutral type containing weakly singular kernels and nonvanishing delays. The discretization of the initial-value problem is based on a reformulation as a sequence of ODEs with nonsmooth solutions. The paper concludes with a brief description of possible alternative numerical approaches for solving various classes of such functional integro-differential equations.

Keywords:

Volterra functional integro-differential equations,
neutral equations,
weakly singular kernels,
variable delays,
collocation methods,
optimal order of convergence.

Mathematics Subject Classification: Primary: 65R20, 65L20, 65L60; Secondary: 34K40, 34K28.

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