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Solving Ordinary Differential Equations with Discontinuities

Editor: Elise de Doncker Authors:

C. W. Gear,

O. OsterbyAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 10, Issue 1

Pages 23 - 44

https://doi.org/10.1145/356068.356071

Published: 01 January 1984 Publication History

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References

[1]

CARVER, M.B. Efficmnt integration over discontinuitms in ordinary differential equation simulations Math Comput Szmul. 20, 3 (1978), 190-196

Google Scholar

[2]

ELLISON, D. Efficient automatic integration of ordinary differential equations with dlscontinuihes. Math. Comput. Simul. 23, 1 (1981), 12-20.

Google Scholar

[3]

GEAR, C.W. Runge-Kutta starters for multlstep methods. ACM Trans Math. Softw 6, 3 (1980), 263-279.

Crossref

Google Scholar

[4]

GEAR, C.W. AND ~)STERB~, O. Solving ordinary differential equations with discontinmties Tech. Rep. R-81-1064, Univ. of Illinois at Urbana-Champaign (1981).

Google Scholar

[5]

HAY, J.L., CROSmE, R.E AND CHAPLIN, R.I. Integration routines for systems with discontinuities Comput. J 17, 3 (1974), 275-278.

Google Scholar

[6]

HINDMARSH, A. GEAR: Ordinary differential equation solver. Tech. Rep UCID-30001, Revision 3, Lawrence Livermore National Laboratories, Livermore, Calif., 1974.

Google Scholar

[7]

MANNSHARDT, R. One-step methods of any order for ordinary difi~rential equations with discontinuous right-hand sides. Numer. Math. 31, 2 (1978), 131-152.

Google Scholar

[8]

MUNTER, P. Numeriske metoder til lcsing of systemer of saedvanlige differentlallignmger indeholdende diskontinulteter. Rapport F40-78.03, Laboratoriet for K~leteknik, Techmcal University of Denmark, 1978 (report is in Damsh)

Google Scholar

[9]

O'REGAN, P.G Step size adjustment at discontinuities for fourth order Runge-Kutta methods. Comput. J 13, 4 (1970), 401-404.

Google Scholar

[10]

THOMSEN, P.G. Numermal simulation in theory and praxis. Mathematics and Computation Tech. Rep. 2/79, Department of Mathematics, University of Trondhelm, Norway 1979.

Google Scholar

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Adams MMuir P(2024)Differential equation software for the computation of error-controlled continuous approximate solutionsNumerical Algorithms10.1007/s11075-024-01784-196:3(1021-1044)Online publication date: 1-Jul-2024
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https://doi.org/10.3934/jcd.2023009
Bagchi S(2023)Analysis of Finite Solution Spaces of Second-Order ODE with Dirac Delta Periodic ForcingAxioms10.3390/axioms1201008512:1(85)Online publication date: 13-Jan-2023
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Index Terms

Solving Ordinary Differential Equations with Discontinuities
1. Mathematics of computing
  1. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 10, Issue 1

March 1984

111 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/356068

Editor:
Elise de Doncker

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1984

Published in TOMS Volume 10, Issue 1

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Hirani AWan AWojtalewicz N(2023)Conservative integrators for piecewise smooth systems with transversal dynamicsJournal of Computational Dynamics10.3934/jcd.2023009(0-0)Online publication date: 2023
https://doi.org/10.3934/jcd.2023009
Bagchi S(2023)Analysis of Finite Solution Spaces of Second-Order ODE with Dirac Delta Periodic ForcingAxioms10.3390/axioms1201008512:1(85)Online publication date: 13-Jan-2023
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Linearization techniques for singular initial-value problems of ordinary differential equations

A computational method for solving boundary value problems for third-order singularly perturbed ordinary differential equations

Differential/algebraic equations as stiff ordinary differential equations

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