Abstract
A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.
Original language | English (US) |
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Pages (from-to) | 209-230 |
Number of pages | 22 |
Journal | Numerical Algorithms |
Volume | 16 |
Issue number | 2 |
DOIs | |
State | Published - 1997 |
Keywords
- DIMSIM methods
- Error accumulation
- Error estimation
- Nordsieck representation
- Variable step-size
ASJC Scopus subject areas
- Applied Mathematics