Efficient Nordsieck second derivative general linear methods: construction and implementation
- 50 Downloads
In this paper, by considering the order conditions for second derivative general linear methods of order p and stage order \(q=p-1\), we investigate construction and implementation of these methods in the Nordsieck form with \(r=s+1=p\), where s and r are the number of internal and external stages of the method, respectively. Constructed methods are A- and L-stable which possess Runge–Kutta stability property. Some numerical experiments are provided in a variable stepsize environment to validate the efficiency of the constructed methods and reliability of the proposed error estimates.
KeywordsStiff differential equations General linear methods Second derivative methods Runge–Kutta stability A- and L-stability Variable stepsize
Mathematics Subject Classification65L05
The results reported in this paper constitute part of the research carried out during the visit of the second author to the University of Tabriz which was supported by the Ministry of Science, Research and Technology of Iran. This author wishes to express her gratitude to A. Abdi for making this visit possible.
- 29.Huang, S.J.Y.: Implementation of general linear methods for stiff ordinary differential equations. Ph.D. thesis, Department of mathematics, The University of Auckland (2005)Google Scholar
- 32.Lee, J.H.J.: Numerical methods for ordinary differential equations: a survey of some standard methods. M.Sc. thesis, Department of mathematics, The University of Auckland (2004)Google Scholar