Research Article
Three Stage MERK Methods for Delay Differential Equations
Issue:
Volume 12, Issue 2, June 2026
Pages:
65-69
Received:
14 March 2026
Accepted:
26 March 2026
Published:
26 May 2026
DOI:
10.11648/j.ijamtp.20261202.11
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Abstract: The application of Runge- Kutta (R-K) methods in obtaining numerical solutions to a wide class of ordinary and partial differential equations arising in various fields of applied sciences has been widely documented. Their efficiency, accuracy, and ease of implementation have made them one of the most popular techniques for solving initial value problems. This success has motivated their extension to more complex systems, particularly Delay Differential Equations (DDEs), which naturally arise in modeling real-life phenomena where time delays are inherent, such as in population dynamics, control systems, epidemiology, and engineering processes. In this paper, we present a numerical approach for solving DDEs by adapting a three-stage Multiderivative Explicit Runge-Kutta (MERK) method. The presence of delayed arguments in DDEs introduces additional computational challenges, especially in the evaluation of past states. To address this, Lagrange interpolation is employed to approximate the delayed terms. Furthermore, the stability properties of the proposed method are investigated through the derivation of the associated stability polynomials. These polynomials provide insight into the convergence behavior and robustness of the methods when applied to stiff and non-stiff delay systems. The performance of these methods are analyzed by solving DDEs, and comparisons are made with existing methods in the literature. The results demonstrate reliability of the three-stage MERK methods for solving DDEs.
Abstract: The application of Runge- Kutta (R-K) methods in obtaining numerical solutions to a wide class of ordinary and partial differential equations arising in various fields of applied sciences has been widely documented. Their efficiency, accuracy, and ease of implementation have made them one of the most popular techniques for solving initial value pro...
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Aleshinloye Zainab Labi
