Abstract
Methods for solving systems of differential equations based on the use of wavelets have become very popular recently. Debeshy wavelets, coiflets were used among others. The disadvantage of such wavelets is that they do not have an analytical expression. Therefore, there are great difficulties in integrating and differentiating expressions containing these wavelets. The article presents an algorithm for the numerical solution of a system of differential equations with variable coefficients based on spline-wavelets on a interval. The algorithm presented generalizes the well-known method based on Haar wavelets which are a special case of spline-wavelets. The results of the article are used to analyze the output processes of multi-dimensional non-stationary linear control systems.
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