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

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