@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 

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}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9134.html} }