Abstract
In this paper, the optimal order of non-confluent Diagonally Implicit Runge-Kutta (DIRK) methods with non-zero weights is examined. It is shown that the order of aq-stage non-confluent DIRK method with non-zero weights cannot exceedq+1. In particular the optimal order of aq stage non-confluent DIRK method with non-zero weights isq+1 for 1≤q≤5. DIRK methods of orders five and six in four and five stages respectively are constructed. It is further shown that the optimal order of a non-confluentq stage DIRK method with non-zero weights isq, forq≥6.
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Al-Rabeh, A.H. Optimal order diagonally implicit Runge-Kutta methods. BIT 33, 619–633 (1993). https://doi.org/10.1007/BF01990538
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DOI: https://doi.org/10.1007/BF01990538