Affiliation:
1. Imperial College, London, UK
Abstract
A new selection is made for an efficient two-step block Runge-Kutta formula of order 6. The new formula is developed using some of the efficiency criteria recently investigated by Shampine, and as a result, a block formula with much improved performance is obtained. An important property of this new formula is that there is a “natural” interpolating polynomial available. This can be used to compute approximate solution values at off-step points without the need to compute any additional function evaluations. The quality of this interpolant is examined, and it is shown to have certain desirable properties. The performance of the new block Runge-Kutta formula is evaluated using the DETEST test set and is shown to be more efficient than certain other standard Runge-Kutta formulas for this particular test set.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference17 articles.
1. Coefficients for the study of Runge-Kutta integration processes;BUTCHER J.C;J. AuNt. Math. Soc.,1963
2. Implicit Runge-Kutta processes;BUTCHER J.C;Math. Comput.,1964
3. Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations;CASH R;Math. Comput.,1983
4. Block embedded explicit Runge-Kutta methods;CASH J.R;Comput. Math. Appl.,1985
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献