Exponential Runge-Kutta methods for delay differential equations

Authors:
Y. Xu;J. J. Zhao;Z. N. Sui
Affiliations:
Department of Mathematics, Harbin Institute of Technology, No. 92, Xi Da Zhi Street, Harbin 150001, Hei Long Jiang, China;Department of Mathematics, Harbin Institute of Technology, No. 92, Xi Da Zhi Street, Harbin 150001, Hei Long Jiang, China;Department of Mathematics, Harbin Institute of Technology, No. 92, Xi Da Zhi Street, Harbin 150001, Hei Long Jiang, China
Venue:
Mathematics and Computers in Simulation
Year:
2010

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Abstract

This paper deals with convergence and stability of exponential Runge-Kutta methods of collocation type for delay differential equations. It is proved that these kinds of numerical methods converge at least with their stage order. Moreover, a sufficient condition of the numerical stability is provided. Finally, some numerical examples are presented to illustrate the main conclusions.