Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639111 | Journal of Computational and Applied Mathematics | 2014 | 15 Pages |
Abstract
A variable stepsize implementation of a recently introduced one-parameter family of high order strongly A-stable Runge-Kutta collocation methods with the first internal stage of explicit type is presented. The so-called SAFERK(α,s) methods with free parameter α and s stages are well-suited for the integration of stiff and differential-algebraic systems, and they are computationally equivalent to the (sâ1)-stage Radau IIA method, since they all have a similar amount of implicitness. For the same number of implicit stages, both SAFERK(α,s) and Radau IIA(sâ1) methods possess algebraic order 2sâ3, whereas the stage order is one unit higher for SAFERK methods. Although there are no L-stable schemes in this method family, the free parameter α can be selected in order to minimize the error coefficients or to maximize the numerical dissipation. Besides a general discussion of the method class, it is shown here how the 4-stage methods can be endowed with an embedded third order formula, and an implementation based on the perfected RADAU5 code with an adaptive stepsize controller proves to be competitive for a wide selection of test problems including electric circuit analysis, constrained mechanical systems, and time-dependent partial differential equations treated by the method of lines.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
S. González-Pinto, D. Hernández-Abreu, B. Simeon,