Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations

被引：2

作者：

Ahmad, N. A. ^{[1
]}

Senu, N. ^{[1
,2
]}

Ibrahim, Z. B. ^{[2
]}

Othman, M. ^{[3
]}

机构：

[1] Univ Putra Malaysia, Inst Math Res, Serdang, Malaysia

[2] Univ Putra Malaysia, Fac Sci, Dept Math & Stat, Serdang, Malaysia

[3] Univ Putra Malaysia, Dept Commun Technol & Network, Serdang, Malaysia

来源：

MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES | 2022年 / 16卷 / 02期

关键词：

diagonally implicit two derivative Runge-Kutta method; delay differential equations; initial value problems; P-stability; Q-stability; P-STABILITY;

D O I：

10.47836/mjms.16.2.04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta 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 (lambda, mu is an element of R) and (mu is an element of C, lambda = 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.

引用

页码：215 / 235

页数：21

共 50 条

[21] Study on Banded Implicit Runge-Kutta Methods for Solving Stiff Differential Equations
Liu, M. Y.
Zhang, L.
Zhang, C. F.
MATHEMATICAL PROBLEMS IN ENGINEERING, 2019, 2019
[22] IMPLICIT RUNGE-KUTTA METHODS FOR DIFFERENTIAL ALGEBRAIC EQUATIONS
ROCHE, M
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1989, 26 (04) : 963 - 975
[23] The parallel three-processor fifth order diagonally implicit Runge-Kutta methods for solving ordinary differential equations
Din, Ummul Khair Salma
Ismail, Fudziah
Suleiman, Mohamed
Majid, Zanariah Abdul
Othman, Mohamed
APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING, 2007, : 184 - +
[24] Stability analysis of explicit and implicit stochastic Runge-Kutta methods for stochastic differential equations
Samsudin, A.
Rosli, N.
Ariffin, A. N.
1ST INTERNATIONAL CONFERENCE ON APPLIED & INDUSTRIAL MATHEMATICS AND STATISTICS 2017 (ICOAIMS 2017), 2017, 890
[25] On the asymptotic stability properties of Runge-Kutta methods for delay differential equations
Nicola Guglielmi
Numerische Mathematik, 1997, 77 : 467 - 485
[26] The stability of natural Runge-Kutta methods for nonlinear delay differential equations
Koto T.
Japan Journal of Industrial and Applied Mathematics, 1997, 14 (1) : 111 - 123
[27] On the asymptotic stability properties of Runge-Kutta methods for delay differential equations
Guglielmi, N
NUMERISCHE MATHEMATIK, 1997, 77 (04) : 467 - 485
[28] THE STABILITY OF A CLASS OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL-EQUATIONS
INTHOUT, KJ
APPLIED NUMERICAL MATHEMATICS, 1992, 9 (3-5) : 347 - 355
[29] Nonlinear stability of Runge-Kutta methods for neutral delay differential equations
Wang, Wan-Sheng
Li, Shou-Fu
Su, Kai
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 214 (01) : 175 - 185
[30] On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations
tHout, KJ
APPLIED NUMERICAL MATHEMATICS, 1996, 22 (1-3) : 237 - 250

← 1 2 3 4 5 →