D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations

Jingjun Zhao, Rui Zhan and Yang Xu

Applied Mathematics and Computation, 2018, vol. 339, issue C, 45-58

Abstract: This paper is concerned with exponential Runge–Kutta methods with Lagrangian interpolation (ERKLMs) for semilinear delay differential equations (DDEs). Concepts of exponential algebraic stability and conditional GDN-stability are introduced. D-convergence and conditional GDN-stability of ERKLMs for semilinear DDEs are investigated. It is shown that exponentially algebraically stable and diagonally stable ERKLMs with stage order p, together with a Lagrangian interpolation of order q (q ≥ p), are D-convergent of order p. It is also shown that exponentially algebraically stable and diagonally stable ERKLMs are conditionally GDN-stable. Some examples of exponentially algebraically stable and diagonally stable ERKLMs of stage order one and two are given, and numerical experiments are presented to illustrate the theoretical results.

Keywords: Exponential Runge–Kutta methods with Lagrangian interpolation; Conditional GDN-stability; D-convergence; Semilinear delay differential equations (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:45-58

DOI: 10.1016/j.amc.2018.07.001

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