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

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