Exponential input‐to‐state stability of delay reaction‐diffusion systems

Ren, Meng-Zhen; Liu, Xiao‐Zhen; Wu, Kai‐Ning

doi:10.1049/cth2.12088

Cited by 2 publications

(1 citation statement)

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“…As another example, the following reaction-diffusion equations with time delay are investigated in [2]:…”

Section: Introductionmentioning

confidence: 99%

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

Zhan

2022

Mathematical Problems in Engineering

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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.

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“…As another example, the following reaction-diffusion equations with time delay are investigated in [2]:…”

Section: Introductionmentioning

confidence: 99%