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Exponential Additive Runge-Kutta Methods for Semi-Linear Differential Equations

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  02 May 2017

Jingjun Zhao ,
Teng Long  and
Yang Xu
Jingjun Zhao*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Teng Long
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Yang Xu*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
*
*Corresponding author. Email addresses:hit_zjj@hit.edu.cn (J. Zhao), yangx@hit.edu.cn (Y. Xu)
*Corresponding author. Email addresses:hit_zjj@hit.edu.cn (J. Zhao), yangx@hit.edu.cn (Y. Xu)
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Abstract

Exponential additive Runge-Kutta methods for solving semi-linear equations are discussed. Related order conditions and stability properties for both explicit and implicit schemes are developed, according to the dimension of the coefficients in the linear terms. Several examples illustrate our theoretical results.

Keywords

Semi-linear differential equationsexponential Runge-Kutta methodsorder conditionsstability

MSC classification

Secondary: 65L20: Stability and convergence of numerical methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 286 - 305
Copyright
Copyright © Global-Science Press 2017 

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