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...
| Main Authors: | , , , |
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| Format: | Article |
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Universiti Putra Malaysia
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/103277/ |
| _version_ | 1848863977899032576 |
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| author | Ahmad, N. A. N., Senu Z. B., Ibrahim M., Othman |
| author_facet | Ahmad, N. A. N., Senu Z. B., Ibrahim M., Othman |
| author_sort | Ahmad, N. A. |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T13:41:30Z |
| format | Article |
| id | upm-103277 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:41:30Z |
| publishDate | 2022 |
| publisher | Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| 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 |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/103277/ http://psasir.upm.edu.my/id/eprint/103277/ http://psasir.upm.edu.my/id/eprint/103277/ |