Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients

Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs is achieved. Specifically, the solutions of QDEs with two-sided coefficients are studied via the adjoint matrix technique. That is, each quaternion can be uniquely expressed as a form of linear combinations of two complex numbers. By applying the complex adjoint representation of quaternion matrix, the connection between QDEs, with unilateral or two-sided coefficients, and a system of ordinary differential equations is achieved. By a novel specific algorithm, the solutions of QDEs with two-sided coefficients are fulfilled. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Qualitative Theory of Dynamical Systems Springer Journals

Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Mathematics, general; Dynamical Systems and Ergodic Theory; Difference and Functional Equations
ISSN
1575-5460
eISSN
1662-3592
D.O.I.
10.1007/s12346-017-0246-z
Publisher site
See Article on Publisher Site

Abstract

The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs is achieved. Specifically, the solutions of QDEs with two-sided coefficients are studied via the adjoint matrix technique. That is, each quaternion can be uniquely expressed as a form of linear combinations of two complex numbers. By applying the complex adjoint representation of quaternion matrix, the connection between QDEs, with unilateral or two-sided coefficients, and a system of ordinary differential equations is achieved. By a novel specific algorithm, the solutions of QDEs with two-sided coefficients are fulfilled.

Journal

Qualitative Theory of Dynamical SystemsSpringer Journals

Published: Jul 11, 2017

References

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