Correcting the results of the numerical integration of differential equations on the basis of the invariance principle. (English. Russian original) Zbl 0841.65072

Comput. Math. Math. Phys. 35, No. 2, 139-149 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 2, 178-191 (1995).
Summary: By considering an analogue or a digital computer as a complex system characterized by a certain level of a priori indeterminacy, on the basis of invariants, \(\varepsilon\)-invariants and generalized invariants of differential equations, the problem of correcting the results of numerical integration of those equations is solved. Efficient methods whereby the results of the approximate integration of ordinary differential equations can be successively refined according to a criterion of increasing accuracy are described.


65L99 Numerical methods for ordinary differential equations
65Y20 Complexity and performance of numerical algorithms