Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

Fathalla A. Rihan; Nasser S. Al-Salti

doi:10.1063/1.4996658

Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

Fathalla A. Rihan^*, Nasser S. Al-Salti

^*Corresponding author for this work

Mathematics & Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

Original language	English
Title of host publication	Mathematical Methods and Computational Techniques in Science and Engineering
Publisher	American Institute of Physics Inc.
Volume	1872
ISBN (Electronic)	9780735415522
DOIs	https://doi.org/10.1063/1.4996658
Publication status	Published - Sep 6 2017
Event	2017 International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2017 - Cambridge, United Kingdom Duration: Feb 24 2017 → Feb 26 2017

Other

Other	2017 International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2017
Country/Territory	United Kingdom
City	Cambridge
Period	2/24/17 → 2/26/17

Keywords

Mono-implicit RK methods
Singularly perturbed problems
Stability
Stiffness
Time-lags

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1063/1.4996658

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Rihan, FA & Al-Salti, NS 2017, Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations. in Mathematical Methods and Computational Techniques in Science and Engineering. vol. 1872, 020001, American Institute of Physics Inc., 2017 International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2017, Cambridge, United Kingdom, 2/24/17. https://doi.org/10.1063/1.4996658

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N2 - In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

AB - In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

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KW - Singularly perturbed problems

KW - Stability

KW - Stiffness

KW - Time-lags

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BT - Mathematical Methods and Computational Techniques in Science and Engineering

PB - American Institute of Physics Inc.

T2 - 2017 International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2017

Y2 - 24 February 2017 through 26 February 2017

ER -

Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

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Keywords

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