Solution of the Neumann Problem with Respect to the Equation for Gravity-Gyroscopic Waves by the Finite Element Method
Abstract
In this paper, on the basis of a numerical finite element method, the solution of the Neumann problem with respect to the oscillation equation for gravity-gyroscopic waves is discussed. The approximation with respect to spatial variables is achieved by using linear splines, and the approximation with respect to time is achieved by using cubic Hermitean splines. It is demonstrated that the use of such approximation with respect to time allows the quality of the solution to be essentially improved as compared with the traditional approximation ensuring the second order accuracy. The stability and accuracy of the method are estimated. Using the method of regularization with spectrum shift, a new method is developed for solving the spatial operator degeneration problem associated with the Neumann problem. The results of the numerical calculations performed provide the possibility to make conclusions on the mode of behavior of the solution of the Neumann problem depending on the problem variables.