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Optimal order diagonally implicit Runge-Kutta methods (1993)

Al-Rabeh, A. H.

Springer

BIT 33 (1993), S. 619-633

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ISSN: 1572-9125

Keywords: 65L05 ; Stiff Ordinary Differential Equations ; Diagonally Implicit Runge-Kutta methods

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01990538

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