Abstract
The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. In this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.
Original language | English (US) |
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Pages (from-to) | 688-712 |
Number of pages | 25 |
Journal | BIT Numerical Mathematics |
Volume | 36 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1996 |
Keywords
- Error estimation
- General linear methods
- Order conditions
- Stage errors
ASJC Scopus subject areas
- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics