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Parallel iterated methods based on multistep Runge-Kutta methods of Radau type (1997)

Burrage, K. ; Suhartanto, H.

Springer

Advances in computational mathematics 7 (1997), S. 37-57

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ISSN: 1572-9044

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract This paper investigates iterated Multistep Runge-Kutta methods of Radau type as a class of explicit methods suitable for parallel implementation. Using the idea of van der Houwen and Sommeijer [18], the method is designed in such a way that the right-hand side evaluations can be computed in parallel. We use stepsize control and variable order based on iterated approximation of the solution. A code is developed and its performance is compared with codes based on iterated Runge-Kutta methods of Gauss type and various Dormand and Prince pairs [15]. The accuracy of some of our methods are comparable with the PIRK10 methods of van der Houwen and Sommeijer [18], but require fewer processors. In addition at very stringent tolerances these new methods are competitive with RK78 pairs in a sequential implementation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1018930415863

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