Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4644851 | Applied Numerical Mathematics | 2016 | 20 Pages |
Abstract
It is well-known that one-step methods have order reduction if they are applied on stiff ODEs such as the example of Prothero–Robinson. In this paper we analyse the local error of Runge–Kutta and Rosenbrock–Wanner methods. We derive new order conditions and define with them BPRBPR-consistency. We show that for strongly A -stable methods BPRBPR-consistency implies BPRBPR-convergence. Finally we analyse methods from literature, derive new BPRBPR-consistent methods and present numerical examples. The numerical and analytical results show the influence of different properties of the methods and of different order conditions on the numerical error and on the numerical convergence order.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Joachim Rang,