期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 256, 期 -, 页码 168-179出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2013.07.027
关键词
Exponential integrators; Exponential Runge-Kutta methods; Stiff order conditions; Error bounds; Semilinear parabolic problems; Stiff problems
资金
- FWF doctoral program 'Computational Interdisciplinary Modelling' [W1227]
- Tiroler Wissenschaftsfond [UNI-0404/1284]
Exponential Runge-Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge-Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method. For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This allows us to obtain the conditions for a method of order 5 in an elegant way. After stating the conditions, we first show that there does not exist an explicit exponential Runge-Kutta method of order 5 with less than or equal to 6 stages. Then, we construct a fifth-order method with 8 stages and prove its convergence for semilinear parabolic problems. Finally, a numerical example is given that illustrates our convergence bound. (C) 2013 Elsevier B.V. All rights reserved.
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