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

H. Brunner; H. Brunner

doi:10.2478/cmam-2008-0015

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

H. Brunner, H. 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

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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title = "Fully Discrete Galerkin Method for Fredholm Integro-Differential Equations with Weakly Singular Kernels",

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.",

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

author = "H. Brunner and H. Brunner",

note = "The research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406). ",

year = "2008",

doi = "10.2478/cmam-2008-0015",

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journal = "Computational Methods in Applied Mathematics",

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T1 - Fully Discrete Galerkin Method for Fredholm Integro-Differential Equations with Weakly Singular Kernels

AU - Brunner, H.

N1 - The research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406).

PY - 2008

Y1 - 2008

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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DO - 10.2478/cmam-2008-0015

M3 - Journal article

AN - SCOPUS:85025266912

SN - 1609-4840

VL - 8

SP - 207

EP - 222

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

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