Malaysian Journal of Mathematical Sciences, May 2022, Vol. 16, No. 2
Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations
Ahmad, N. A., Senu, N., Ibrahim, Z. B., and Othman, M.
Corresponding Email: nuramirah_ahmad@yahoo.com
Received date: 19 June 2021
Accepted date: 29 December 2021
Abstract:
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 $(\lambda, \mu \in \Re)$ and $(\mu \in \mathbb{C} , \lambda=0)$ are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (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.
Keywords: diagonally implicit two derivative Runge-Kutta method; delay differential equations; initial value problems; P-stability; Q-stability.
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