TY - JOUR
T1 - Implementation of DIMSIMs for stiff differential systems
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
✩ This work was supported by the National Science Foundation grant NSF DMS-9971164. E-mail address: jackiewi@math.la.asu.edu (Z. Jackiewicz).
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
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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 -