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Linear Multistep Methods for Volterra Integro-Differential Equations

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Peter LinzAuthors Info & Claims

Journal of the ACM (JACM), Volume 16, Issue 2

Pages 295 - 301

https://doi.org/10.1145/321510.321521

Published: 01 April 1969 Publication History

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Abstract

The Dahlquist stability analysis for ordinary differential equations is extended to the case of Volterra integro-differential equations. Thus the standard multistep methods can be generalized to furnish algorithms for solving integro-differential equations. Special starting procedures are discussed, and some numerical examples are presented.

References

[1]

DAHLQUIST, G. Convergence and stability in the numerical integration of ordinary differential equations. Math. Seand. 4 (1956), 33-53.

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[2]

DAVIS, H. T. Introduction to Nonlinear Differential and Integral Equations. Dover, New York, 1962.

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[3]

DAY, J .T . Note on the numerical solution of integro-differential equations. Comput. J. 9, 4 (Feb. 1967), 394-395.

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[4]

HENRICI, P. Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.

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[5]

POUZET, P. MEthode d'intEgration numdrique des dquations integrales et intdgro-differentielles du type de Volterra de seconde espece. Formules de Runge-Kutta, Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integrodifferential Equations, Rome, 1960, pp. 362-368.

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Ibrahimov VMehdiyeva GImanova MJuraev D(2023)Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential EquationsWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2023.22.8622(781-791)Online publication date: 20-Oct-2023
https://doi.org/10.37394/23206.2023.22.86
Ibrahimov VImanova M(2023)The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special StructureWSEAS TRANSACTIONS ON SYSTEMS10.37394/23202.2023.22.2022(199-206)Online publication date: 9-Mar-2023
https://doi.org/10.37394/23202.2023.22.20
Baker CPaul CWillé D(2023)Issues in the numerical solution of evolutionary delay differential equationsAdvances in Computational Mathematics10.1007/BF029886253:1(171-196)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF02988625
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Index Terms

Linear Multistep Methods for Volterra Integro-Differential Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Integral equations

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Information

Published In

Journal of the ACM Volume 16, Issue 2

April 1969

157 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321510

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1969

Published in JACM Volume 16, Issue 2

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Ibrahimov VMehdiyeva GImanova MJuraev D(2023)Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential EquationsWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2023.22.8622(781-791)Online publication date: 20-Oct-2023
https://doi.org/10.37394/23206.2023.22.86
Ibrahimov VImanova M(2023)The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special StructureWSEAS TRANSACTIONS ON SYSTEMS10.37394/23202.2023.22.2022(199-206)Online publication date: 9-Mar-2023
https://doi.org/10.37394/23202.2023.22.20
Baker CPaul CWillé D(2023)Issues in the numerical solution of evolutionary delay differential equationsAdvances in Computational Mathematics10.1007/BF029886253:1(171-196)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF02988625
Farhloul MFortin M(2023)A mixed finite element for the stokes problem using quadrilateral elementsAdvances in Computational Mathematics10.1007/BF024319983:1-2(101-113)Online publication date: 22-Mar-2023
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Robinson PDunn IReichman D(2022)Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansionPhysical Review B10.1103/PhysRevB.105.224305105:22Online publication date: 7-Jun-2022
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IYANDA FISMAEL BABDULGAFAR T(2021)Numerical Assessment of Symmetric and Non-Symmetric Kernel Functions on Second Order Non-Homogenous Volterra Integro-Differential EquationsSakarya University Journal of Science10.16984/saufenbilder.66829925:6(1263-1274)Online publication date: 31-Dec-2021
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Almasoodi AAbdi AHojjati G(2021)A GLMs-based difference-quadrature scheme for Volterra integro-differential equationsApplied Numerical Mathematics10.1016/j.apnum.2021.02.001163(292-302)Online publication date: May-2021
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Mehdiyeva GIbrahimov VImanova M(2020)On some comparison of multistep second derivative methods with the multistep hybrid methods and their application to solve integro-differiential equationsJournal of Physics: Conference Series10.1088/1742-6596/1564/1/0120161564(012016)Online publication date: 30-Jun-2020
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Egger HSchmidt KShashkov V(2020)Multistep and Runge–Kutta convolution quadrature methods for coupled dynamical systemsJournal of Computational and Applied Mathematics10.1016/j.cam.2019.112618(112618)Online publication date: Jan-2020
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Mehdiyeva GIbrahimov VImanova M(2019)On some comparison of the multistep hybrid methods and their application solving of the Volterra integro-differential equationsJournal of Physics: Conference Series10.1088/1742-6596/1334/1/0120071334(012007)Online publication date: 18-Oct-2019
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Abstract

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Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods

Multistep collocation methods for Volterra integro-differential equations

Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations

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