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Block Runge‐Kutta Methods on Parallel Computers
Author(s) -
van der Houwen P. J.,
Sommeijer B. P.
Publication year - 1992
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19920720102
Subject(s) - equidistant , block (permutation group theory) , runge–kutta methods , ode , computer science , mathematics , algorithm , computational science , parallel computing , numerical analysis , mathematical analysis , geometry
In this paper block methods for solving ODEs on parallel computers are constructed. Most block methods found in the literature produce approximations to the exact solution at equidistant points. Here, we allow that the approximations correspond to nonequidistant points like the intermediate approximations computed in Runge‐Kutta methods. This approach enables us to improve the order of accuracy. We concentrate on explicit methods such that they are suitable for use on parallel computers.