Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

An Approach to the Construction of Two-sided Estimates for Sets of Solutions of Nonlinear Differential Equations with Interval Parameters by Projection Methods

Author(s):

Alexander Anatolievich Rogoza

Bauman Moscow State Technical University (BMSTU),
Kaluga, Bazenova st, 2.

aemaeth_eternity@mail.ru

Abstract:

The paper deals with issues related to the construction of two-sided estimates of the solution sets of systems of nonlinear differential equations with interval parameters. The convergence of interval estimates to the set of exact solutions in the Hausdorff metric has been substantiated. Theorems on coordinate wise convergence to the set of exact solutions have been proved. Thus, the proposed approach allows us to deal with wrapping effect. The algorithm constructs the approximate solutions of this problem by using analytical formulas obtained by projection methods. It is essential that the constructed approximation takes into account the global error interval estimate, which results in getting a guaranteed evaluation.

Keywords

• inclusion of the solution set
• interval extension
• interval method of successive approximations
• projection methods

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