Abstract
This article discusses the interval variant of solving ordinary differential equations with given initial conditions, i.e. the Cauchy problem, by the method of operational calculus. This is where the interval version of the operational calculus is motivated and built. As a result, on the basis of the proved theorem in this article, an analytic interval set of solutions is obtained that is guaranteed to contain a real solution to the problem.
Highlights
When solving most technical problems, its mathematical model is reduced to differential equations
The use of interval methods allows one to obtain guaranteed two-sided estimates for solutions of differential equations, but the practical calculation of these estimates is associated with the problem of exponential mutual divergence of the found boundaries - a phenomenon that received the name of the wrapping effect [1, 2]
The proposed method of operational calculus is motivated by the fact that when using this method to solve ordinary differential equations (ODE) with given initial conditions (Cauchy problems), only four arithmetic operations and a ready-to-use table of transition from one type of function to another and back are applied
Summary
When solving most technical problems, its mathematical model is reduced to differential equations. The use of interval methods allows one to obtain guaranteed two-sided estimates for solutions of differential equations, but the practical calculation of these estimates is associated with the problem of exponential mutual divergence of the found boundaries - a phenomenon that received the name of the wrapping effect (in the English-language literature - the wrapping effect, and in Russian works the names often appear - the wrapping effect or the Moore effect) [1, 2]. From the course of higher mathematics, methods of operational calculus are used to solve ODEs or systems of ODEs with initial conditions, i.e. for solutions of the Cauchy problem. We will briefly outline the real version of the statement of the Cauchy problem and its solution by the method of operational calculus
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Multidisciplinary Research and Analysis
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
