Abstract
This paper deals with the systems of algebraic equations arising in the application ofB-stable Runge-Kutta methods. It is shown that under natural assumptions such systems do not always have a solution. In addition, general sufficient conditions are presented under which such systems do have unique solutions.
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Crouzeix, M., Hundsdorfer, W.H. & Spijker, M.N. On the existence of solutions to the algebraic equations in implicit runge-kutta methods. BIT 23, 84–91 (1983). https://doi.org/10.1007/BF01937328
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DOI: https://doi.org/10.1007/BF01937328