Selšuk Journal of Applied Mathematics

 Selšuk Journal of
  Applied Mathematics

  Winter-Spring, 2001
  Volume  2
  Number 1

Research Center of 
  Applied Mathematics

 SJAM Winter-Spring 2001, Volume 2 - Number 1

On a global error estimate in long-term numerical integration of ordinary differential equations*

Gennadii A. Chumakov1* ,  Natalia A. Chumakova 2

1 Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

 2 Boreskov Institute of Catalysis, SB RAS, Pr. Ak. Lavrentieva 5, Novosibirsk, Russia

Received: March 06, 2001

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.

Key words
numerical solution of ODEs, Runge-Kutta methods, global error, chemical kinetic model

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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