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Volume 17, Issue 6
Order Results for Algebraically Stable Mono-Implicit Runge-Kutta Methods

Ai-Guo Xiao

J. Comp. Math., 17 (1999), pp. 639-644.

Published online: 1999-12

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  • Abstract

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage(1994) has shown that the order of an s-stage mono-implicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min $(\widetilde{s}, 4)$, and the stage order together with the optimal B-convergence order is at most min(s,2), where 

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@Article{JCM-17-639, author = {Xiao , Ai-Guo}, title = {Order Results for Algebraically Stable Mono-Implicit Runge-Kutta Methods}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {6}, pages = {639--644}, abstract = {

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage(1994) has shown that the order of an s-stage mono-implicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min $(\widetilde{s}, 4)$, and the stage order together with the optimal B-convergence order is at most min(s,2), where 

image.png

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9134.html} }
TY - JOUR T1 - Order Results for Algebraically Stable Mono-Implicit Runge-Kutta Methods AU - Xiao , Ai-Guo JO - Journal of Computational Mathematics VL - 6 SP - 639 EP - 644 PY - 1999 DA - 1999/12 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9134.html KW - AB -

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage(1994) has shown that the order of an s-stage mono-implicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min $(\widetilde{s}, 4)$, and the stage order together with the optimal B-convergence order is at most min(s,2), where 

image.png

Xiao , Ai-Guo. (1999). Order Results for Algebraically Stable Mono-Implicit Runge-Kutta Methods. Journal of Computational Mathematics. 17 (6). 639-644. doi:
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