On exact solutions of a class of interval boundary value problems

Title:

On exact solutions of a class of interval boundary value problems

Creator:

Gasilov, Nizami A.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3d6ffd9c-081c-41a6-9c91-734e28e2a7ac
uuid:3d6ffd9c-081c-41a6-9c91-734e28e2a7ac
doi:10.14736/kyb-2022-3-0376

Subject:

interval differential equations, boundary value problem, bunch of functions, and linear differential equations

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the proposed approach is that the solution is treated as a set of real functions, not as an interval-valued function, as usual. It is well-known that the existence and uniqueness of the solution is a critical issue, especially in studying BVPs. We provide an existence and uniqueness result for interval BVPs under consideration. We also present a numerical method to compute the lower and upper bounds of the solution bunch. Moreover, we express the solution by an analytical formula under certain conditions. We provide numerical examples to illustrate the effectiveness of the introduced approach and the proposed method. We also demonstrate that the approach is applicable to non-linear interval BVPs.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

376-399

Source:

Kybernetika | 2022 Volume:58 | Number:3

Harvested from:

CDK

Metadata only:

false