RIGOROUS COMPUTATIONAL SHADOWING OF ORBITS OF ORDINARY DIFFERENTIAL-EQUATIONS

The existence of a true orbit near a numerically computed approximate orbit - shadowing - of autonomous system of ordinary differential equations is investigated. A general shadowing theorem for finite time, which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the approximate orbit in terms of computable quantities, is proved. The practical use and the effectiveness of this theorem is demonstrated in the numerical computations of chaotic orbits of the Lorenz equations.