Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain

Affiliation(s)

National Aviation University, Kyiv, Ukraine.

Berdakh Kara-Kalpak State University, Nukus, Uzbekistan.

National Aviation University, Kyiv, Ukraine.

Berdakh Kara-Kalpak State University, Nukus, Uzbekistan.

Abstract

To solve the equation for gravity-gyroscopic waves in a rectangular domain, the distinguished algorithm for the solution of the Cauchy problem for a second-order transient equation is proposed. This algorithm is developed by using the time-varying finite element method. The space derivatives in the gravity-gyroscopic wave equation are approximated with finite differences. The stability and accuracy of the method are estimated. The procedure for the implementation of the method is developed. The calculations were performed for determining the steady-state modes of fluctuations of the solutions of the gravity-gyroscopic wave equation depending on the problem parameters.

Cite this paper

Moskalkov, M. and Utebaev, D. (2014) Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain.*Applied Mathematics*, **5**, 1120-1132. doi: 10.4236/am.2014.58105.

Moskalkov, M. and Utebaev, D. (2014) Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain.

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