Norges Teknisk-naturvitenskapelige Universitet Cost Efficient Lie Group Integrators in the Rkmk Class Cost Efficient Lie Group Integrators in the Rkmk Class
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چکیده
In this work a systematic procedure is implemented in order to minimise the computational cost of the Runge–Kutta–Munthe-Kaas (RKMK) class of Lie-group solvers. The process consists of the application of a linear transformation to the stages of the method and the analysis of a graded free Lie algebra to reduce the number of commutators involved. We consider here RKMK integration methods up to order seven based on some of the most popular Runge–Kutta schemes. Departament de Matemàtiques, Universitat Jaume I, 12071-Castellón, Spain. Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway, and Center for Advanced Study, Drammensveien 78, 0271 Oslo, Norway. AMS Subject Classification: 65L05
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تاریخ انتشار 2002