Abstract
Some issues related to the implementation of diagonally implicit multistage integration methods for stiff differential systems are discussed. They include reliable estimation of the local discretization error, construction of continuous interpolants, solution of nonlinear systems of equations by simplified Newton iterations, choice of initial stepsize and order, and step and order changing strategy. Numerical results are presented which indicate that an experimental Matlab code based on type 2 methods of order one, two and three outperforms ode15s code from Matlab ODE suite on problems whose Jacobian has eigenvalues which are close to the imaginary axis.
Original language | English (US) |
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Pages (from-to) | 251-267 |
Number of pages | 17 |
Journal | Applied Numerical Mathematics |
Volume | 42 |
Issue number | 1-3 |
DOIs | |
State | Published - Aug 1 2002 |
Keywords
- DIMSIMs
- Local error estimation for stiff systems
- Nordsieck representation
- Simplified Newton iterations
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics