Fully Discrete Galerkin Method for Fredholm Integro-Differential Equations with Weakly Singular Kernels

H. Brunner; Hermann BRUNNER

doi:10.2478/cmam-2008-0015

Fully Discrete Galerkin Method for Fredholm Integro-Differential Equations with Weakly Singular Kernels

H. Brunner, Hermann BRUNNER

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θ_j(t) = q_jt (0 < q₁< … < q_r< 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.

Original language	English
Pages (from-to)	207-222
Number of pages	16
Journal	Computational Methods in Applied Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.2478/cmam-2008-0015
Publication status	Published - 2008

Scopus Subject Areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

User-Defined Keywords

collocation solutions
multiple vanishing delays
optimal order of superconvergence
solution representations
uniform meshes
Volterra functional integral and integro-differential equations

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10.2478/cmam-2008-0015

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abstract = "We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1< … < qr< 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.",

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AU - Brunner, H.

AU - BRUNNER, Hermann

PY - 2008

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N2 - We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1< … < qr< 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.

AB - We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1< … < qr< 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.

KW - collocation solutions

KW - multiple vanishing delays

KW - optimal order of superconvergence

KW - solution representations

KW - uniform meshes

KW - Volterra functional integral and integro-differential equations

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VL - 8

SP - 207

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JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

IS - 3

ER -

Fully Discrete Galerkin Method for Fredholm Integro-Differential Equations with Weakly Singular Kernels

Abstract

Scopus Subject Areas

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