Mühendislik Fakültesi / Faculty of Engineering

Permanent URI for this collectionhttps://hdl.handle.net/11727/1401

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Subject: search.filters.subject.bunch of functions

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    On the Numerical Solution of Linear Differential Equations with Interval Coefficients
    (2017) Gasilov, N. A.; Amrahov, S. E.; https://orcid.org/0000-0001-7747-5467; AEN-1756-2022; AAF-3339-2020
    In this study, we consider Initial Value Problem (IVP) for a linear differential equation with interval coefficients. The initial values of the problem are taken as intervals, too. We interpret the interval IVP as a set of classical IVPs, and we investigate the bunch (set) of their solutions. We define this bunch to be the solution of the interval IVP. We develop a numerical method to find the upper and lower bounds of the solution bunch. We apply the method to an example and illustrate the solution.
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    On Exact Solutions Of A Class Of Interval Boundary Value Problems
    (2022) Gasilov, Nizami A.
    In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differ-ential 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.
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    On differential equations with interval coefficients
    (2019) Gasilov, Nizami A.; Amrahov, Sahin Emrah; AAN-9386-2020
    In this study, a new approach is developed to solve the initial value problem for interval linear differential equations. In the considered problem, the coefficients and the initial values are constant intervals. In the developed approach, there is no need to define a derivative for interval-valued functions. All derivatives used in the approach are classical derivatives of real functions. The reason for this is that the solution of the problem is defined as a bunch of real functions. Such a solution concept is compatible also with the robust stability concept. Sufficient conditions are provided for the solution to be expressed analytically. In addition, on a numerical example, the solution obtained by the proposed approach is compared with the solution obtained by the generalized Hukuhara differentiability. It is shown that the proposed approach gives a new type of solution. The main advantage of the proposed approach is that the solution to the considered interval initial value problem exists and is unique, as in the real case.