Analysis of Exponential Runge–Kutta Methods for Differential Equations with Time Delay

Rui Zhan and Abid_ Hussanan

Mathematical Problems in Engineering, 2022, vol. 2022, 1-11

Abstract: Numerous mathematical models simulating the phenomenon in science and engineering use delay differential equations. In this paper, we focus on the semilinear delay differential equations, which include a wide range of mathematical models with time lags, such as reaction-diffusion equation with delay, model of bacteriophage predation on bacteria in a chemostat, and so on. This paper is concerned with the stability and convergence properties of exponential Runge–Kutta methods for semilinear delay differential equations. GDN-stability and D-convergence of exponential Runge–Kutta methods are investigated. These two concepts are generalizations of the classical AN-stability and B-convergence for ordinary differential equations to delay differential equations. Sufficient conditions for GDN-stability are given by a newly introduced concept of strong exponential algebraic stability. Further, with the aid of diagonal stability, we show that exponential Runge–Kutta methods are D-convergent. The D-convergent orders are also examined. Numerical experiments are presented to illustrate the theoretical results.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:2693940

DOI: 10.1155/2022/2693940

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