Mathematical modeling of oscillatory processes with a free boundary
Abstract
Introduction. The paper is devoted to research of the wave processes with free boundary based on the finite-difference method. Materials and methods. A mathematical model describing the dynamics of distribution of wave fluctuation was proposed on the basis of heterogeneous wave equation with the appropriate initial and boundary conditions. Discretization of the model was conducted using the integro-interpolation method taking into account the partial "filling" of computational cells. The adaptive modified alternating triangular iterative method of variational type with the highest rate of convergence in the class of two-layer iterative methods for solving the developed difference equations. Results. The developed discrete mathematical model for numerical simulation of wave propagation. The results of numerical experiments were obtained. The developed numerical algorithms and their computer implementation were used to research the dynamics of distribution of wave processes in the presence of the free boundary. Discussion and conclusions. The obtained results can be used for research of the dynamics of distribution of the wave processes with a free boundary and controlling in conducting experimental researches, evaluation and diagnosis, etc.
Keywords
Supporting agencies: The paper was supported by RFFR project № 15-07-08626, № 15-01-08619.
About the Authors
Alexander Ev. Chistyakov
Don State Technical University
(1 Gagarin sq., Rostov-on-Don, Russian Federation)
Russian Federation
Russian Federation
Chistyakov Alexander Ev., Professor, Department "Software computer engineering and automated systems", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths.
Elena An. Protsenko
Taganrog Institute named after A. P. Chekhov (branch) of Rostov state University (RINE)
(48 Initiative St., Taganrog, Russian Federation)
Russian Federation
Russian Federation
Protsenko Elena An., Associate Professor, Mathematics Department, Taganrog Institute named after A. P. Chekhov (branch) of Rostov state University (RINE) (48 Initiative St., Taganrog, Russian Federation), Candidate of Science in Physics and Maths.
Elena F. Timofeeva
North Caucasus State Technical University
(2, Kulakov Pr., Stavropol, 355029, Russian Federation)
Russian Federation
Russian Federation
Timofeeva Elena F., Associate Professor, Department of Applied Mathematics and Computer Technology, North Caucasus State Technical University (2, Kulakov Pr., Stavropol, 355029, Russian Federation), Candidate of Science in Physics and Maths
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Review
For citations:
Chistyakov A.E., Protsenko E.A., Timofeeva E.F. Mathematical modeling of oscillatory processes with a free boundary. Computational Mathematics and Information Technologies. 2017;1(1).
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