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On algorithm of numerical modelling of the Boussinesq – L’ove waves
A.A. Zamyshlyaeva, South Ural State University, Chelyabinsk, Russian Federation, email@example.com
The article is devoted to the description of the software complex «Modeling of the Boussinesq – L’ove waves», which consists of four modules and implements the algorithm of numerical solution of the problem Showalter - Sidorov (Cauchy) with Dirichlet condition on a segment, on a graph, in a rectangle or a circle (user selectable) for the Boussinesq – L’ove equation, depending on the coefficients and the initial data. Specified equation models the longitudinal fluctuations in the elastic rod (in case of a segment), in construction (case of graph), propagation of waves in shallow water or in dispersive environments (case of rectangle or circle). The algorithm implemented the method of phase space and modified Galerkin method. In each of the four modules the eigenvalues and the eigenfunctions for the Laplace operator in the relevant domain are computed, the solution in the form of Galerkin sum by the first several eigenfunctions is found. The program allows drawing a graph for the numerical solution of the specified problems. The results may be useful for specialists in the field of mathematical physics and mathematical modeling.
Showalter – Sidorov problem, Boussinesq – L’ove equation, Sobolev type equation, phase space method, Galerkin method
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