Highly stable implicit-explicit Runge-Kutta methods

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• 作者：Giuseppe Izzo^a ; ¹ ; ^{giuseppe.izzo@unina.it} ; Zdzislaw Jackiewicz^b ; ^c ; ^{jackiewicz@asu.edu}
• 关键词：Runge&ndash ; Kutta methods ; Implicit&ndash ; explicit methods ; Stability analysis ; Strong stability preserving ; Courant&ndash ; Friedrichs&ndash ; Levy condition ; Hyperbolic conservation laws
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：113
• 期：Complete
• 页码：71-92
• 全文大小：1504 K
• 卷排序：113

文摘

We investigate implicit–explicit (IMEX) Runge–Kutta (RK) methods for differential systems with non-stiff and stiff processes. The construction of such methods with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is A  -stable, is described. We also describe the construction of IMEX RK methods, where the ‘explicit part’ of the schemes have strong stability properties. Examples of highly stable IMEX RK methods are provided up to the order p=4p=4. Numerical examples are also given which illustrate good performance of these schemes.