Abstract
To overcome known disadvantages in the use of singly-implicit methods in the solution of stiff differential equations, two generalizations have been recently introduced. These are the use of additional diagonally-implicit stages and the use of effective order as a weakening of the conditions on the method. In this paper, these two generalizations are combined into a unified scheme. The resulting DESIRE methods are very promising alternatives to standard methods for solving stiff problems.
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Butcher, J., Diamantakis, M. DESIRE: diagonally extended singly implicit Runge–Kutta effective order methods. Numerical Algorithms 17, 121–145 (1998). https://doi.org/10.1023/A:1011623226983
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DOI: https://doi.org/10.1023/A:1011623226983