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Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations

The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative RungeKutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their...

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Main Authors: Ahmad, N. A., N., Senu, Z. B., Ibrahim, M., Othman
Format: Article
Published: Universiti Putra Malaysia 2022
Online Access:http://psasir.upm.edu.my/id/eprint/103277/
https://mjms.upm.edu.my/senaraimakalah.php?yr=2022&bln=May&vol=16&no=2
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spelling my.upm.eprints.1032772023-11-07T04:37:38Z http://psasir.upm.edu.my/id/eprint/103277/ Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations Ahmad, N. A. N., Senu Z. B., Ibrahim M., Othman The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative RungeKutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ, µ ∈ <) and (µ ∈ C, λ = 0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit RungeKutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration. Universiti Putra Malaysia 2022 Article PeerReviewed Ahmad, N. A. and N., Senu and Z. B., Ibrahim and M., Othman (2022) Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations. Malaysian Journal of Mathematical Sciences, 16 (2). 215 - 235. ISSN 1823-8343 https://mjms.upm.edu.my/senaraimakalah.php?yr=2022&bln=May&vol=16&no=2 10.47836/mjms.16.2.04
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative RungeKutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ, µ ∈ <) and (µ ∈ C, λ = 0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit RungeKutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.
format Article
author Ahmad, N. A.
N., Senu
Z. B., Ibrahim
M., Othman
spellingShingle Ahmad, N. A.
N., Senu
Z. B., Ibrahim
M., Othman
Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
author_facet Ahmad, N. A.
N., Senu
Z. B., Ibrahim
M., Othman
author_sort Ahmad, N. A.
title Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
title_short Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
title_full Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
title_fullStr Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
title_full_unstemmed Stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
title_sort stability analysis of diagonally implicit two derivative runge-kutta methods for solving delay differential equations
publisher Universiti Putra Malaysia
publishDate 2022
url http://psasir.upm.edu.my/id/eprint/103277/
https://mjms.upm.edu.my/senaraimakalah.php?yr=2022&bln=May&vol=16&no=2
_version_ 1783879947154096128
score 13.159267

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