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Selçuk Journal
of
Applied Mathematics
Winter-Spring, 2001
Volume 2
Number 1
Research Center
of
Applied Mathematics
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SJAM
Winter-Spring 2001, Volume 2 - Number 1
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On a global error estimate in long-term numerical
integration of ordinary differential equations *
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Gennadii A. Chumakov1* , Natalia A. Chumakova 2 |
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1
Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
email: chumakov@math.nsc.ru
2
Boreskov Institute of Catalysis, SB RAS, Pr. Ak. Lavrentieva 5,
Novosibirsk, Russia
email: chum@catalysis.nsk.su
Received: March 06, 2001
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Summary
We
describe an effective computational procedure of obtaining estimate
for the global error in the long-term numerical integration with one-step
embedded explicit Runge-Kutta methods applied to an ODE system. The
paper relies on the existence of an asymptotic expansion for the
global error. An example is given using a particular ODE system
modeling the behavior of a heterogeneous catalytic reaction with
complex dynamics.
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Key
words
numerical solution of ODEs, Runge-Kutta methods, global error,
chemical kinetic model
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Mathematics Subject Classification (1991):
65-01,
65L06, 65Y99
*
The research was supported in part by the International Association
for the promotion of co-operation with scientists from the New
Independent States of the former Soviet Union (INTAS) grant No.
99-01882.
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Article
in PS format (8607 kb) |
Article in ZIP
format (502 kb) |
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