On the construction of second derivative diagonally implicit multistage integration methods for ODEs

Authors:
A. Abdi;M. Bra;G. Hojjati
Affiliations:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran;AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30059 Kraków, Poland;Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Venue:
Applied Numerical Mathematics
Year:
2014

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Abstract

Second derivative diagonally implicit multistage integration methods (SDIMSIMs) as a subclass of second derivative general linear methods (SGLMs) have been divided into four types, depending on the nature of the differential system to be solved and the computer architecture that is used to implement these methods. In this paper, we describe the construction of SDIMSIMs for all types with Runge-Kutta stability property. Examples of (p,q,r,s) SDIMSIMs are given with p=q=r=s=