The existence of a true orbit near a numericallycomputed approximate orbit -- shadowing -- ofautonomous system of ordinary differential equationsis investigated.A general shadowing theorem for finite time,which guarantees the existence of shadowingin ordinary differential equationsand provides error bounds for the distance betweenthe true and the approximate orbit in terms of computablequantities, is proved.The practical use and the effectiveness of this theoremis demonstrated in the numerical computationsof chaotic orbits of the Lorenz equations.
- Mathematics Subject Classification (1991): 65L05
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics