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) |
|---|---|
| Pages (from-to) | 251-267 |
| Number of pages | 17 |
| Journal | Applied Numerical Mathematics |
| Volume | 42 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Aug 2002 |
Fingerprint
Keywords
- DIMSIMs
- Local error estimation for stiff systems
- Nordsieck representation
- Simplified Newton iterations
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation
Cite this
Implementation of DIMSIMs for stiff differential systems. / Jackiewicz, Zdzislaw.
In: Applied Numerical Mathematics, Vol. 42, No. 1-3, 08.2002, p. 251-267.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Implementation of DIMSIMs for stiff differential systems
AU - Jackiewicz, Zdzislaw
PY - 2002/8
Y1 - 2002/8
N2 - 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.
AB - 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.
KW - DIMSIMs
KW - Local error estimation for stiff systems
KW - Nordsieck representation
KW - Simplified Newton iterations
UR - http://www.scopus.com/inward/record.url?scp=0036679991&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036679991&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(01)00154-4
DO - 10.1016/S0168-9274(01)00154-4
M3 - Article
AN - SCOPUS:0036679991
VL - 42
SP - 251
EP - 267
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 1-3
ER -