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Soft Computing

, Volume 22, Issue 12, pp 3817–3828

Solving a nonhomogeneous linear system of interval differential equations

• Nizami A. Gasilov
• Şahin Emrah Amrahov
Foundations

Abstract

In most application problems, the exact values of the input parameters are unknown, but the intervals in which these values lie can be determined. In such problems, the dynamics of the system are described by an interval-valued differential equation. In this study, we present a new approach to nonhomogeneous systems of interval differential equations. We consider linear differential equations with real coefficients, but with interval initial values and forcing terms that are sets of real functions. For each forcing term, we assume these real functions to be linearly distributed between two given real functions. We seek solutions not as a vector of interval-valued functions, as usual, but as a set of real vector functions. We develop a method to find the solution and establish an existence and uniqueness theorem. We explain our approach and solution method through an illustrative example. Further, we demonstrate the advantages of the proposed approach over the differential inclusion approach and the generalized differentiability approach.

Keywords

Interval differential equation Linear system of differential equations Set of functions

Notes

Acknowledgements

We are grateful to the editor and the anonymous reviewers for their comments and suggestions, which helped to improve the quality of this paper.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

1. 1.Baskent UniversityAnkaraTurkey
2. 2.Computer Engineering DepartmentAnkara UniversityAnkaraTurkey