Unconditionally Strong Stability Preserving Extensions of the TR-BDF2 Method

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• 作者：L. Bonaventura ; A. Della Rocca
• 关键词：TR ; BDF2 ; Runge–Kutta ; Absolute monotonicity ; Positivity preservation ; TVD ; SSP
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：70
• 期：2
• 页码：859-895
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. In order to achieve unconditional monotonicity, hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy, while keeping the native L-stability property, which is useful for the application to stiff problems. Numerical experiments compare these different hybridization strategies to other methods used in stiff and mildly stiff problems. The results show that the proposed strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in literature.