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June  2006, 5(2): 261-276. doi: 10.3934/cpaa.2006.5.261

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, Canada

Received  February 2005 Revised  May 2005 Published  March 2006

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: weakly singular kernels, variable delays, Volterra functional integro-differential equations, collocation methods, optimal order of convergence., neutral equations.
Mathematics Subject Classification: Primary: 65R20, 65L20, 65L60; Secondary: 34K40, 34K2.
Citation: Hermann Brunner. The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Communications on Pure & Applied Analysis, 2006, 5 (2) : 261-276. doi: 10.3934/cpaa.2006.5.261
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