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

Hermann BRUNNER

doi:10.3934/cpaa.2006.5.261

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

Hermann BRUNNER^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	261-276
Number of pages	16
Journal	Communications on Pure and Applied Analysis
Volume	5
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2006.5.261
Publication status	Published - Jun 2006

Scopus Subject Areas

Analysis
Applied Mathematics

User-Defined Keywords

Collocation methods
Neutral equations
Optimal order of convergence
Variable delays
Volterra functional integro-differential equations
Weakly singular kernels

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10.3934/cpaa.2006.5.261

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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.",

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AB - 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.

KW - Collocation methods

KW - Neutral equations

KW - Optimal order of convergence

KW - Variable delays

KW - Volterra functional integro-differential equations

KW - Weakly singular kernels

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

Abstract

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