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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 4, Pages 145–150 (Mi vyuru410)  

Short Notes

Approximation of solutions to the boundary value problems for the generalized Boussinesq equation

V. Z. Furaevab, A. I. Antonenkob

a South Ural State University, Chelyabinsk, Russian Federation
b Novokuznetsk Institute (branch) Kemerovo State University, Novokuznetsk, Russian Federation

Abstract: The paper is devoted to one of the Sobolev type mathematical models of fluid filtration in a porous layer. Results that allow to obtain numerical solutions are significant for applied problems. We propose the following algorithm to solve the initial-boundary value problems describing the motion of a free surface filtered in a fluid layer having finite depth. First, the boundary value problems are reduced to the Cauchy problems for integro-differential equations, and then the problems are numerically integrated. However, numerous computational experiments show that the algorithm can be simplified by replacing the integro-differential equations with the corresponding approximating Riccati differential equations, whose solutions can also be found explicitly. In this case, the numerical values of the solution to the integro-differential equation are concluded between successive values of approximating solutions. Therefore, we can pointwise estimate the approximation errors. Examples of results of numerical integration and corresponding approximations are given.

Keywords: Sobolev type equation; boundary value problem; integro-differential equation; free surface; Riccati equation.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.А03.21.0011
The work was supported by Act 211 Government of the Russian Federation, contract No. 02.А03.21.0011.


DOI: https://doi.org/10.14529/mmp170414

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Bibliographic databases:

UDC: 517.95
MSC: 35Q79, 35A35
Received: 22.10.2017
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Citation: V. Z. Furaev, A. I. Antonenko, “Approximation of solutions to the boundary value problems for the generalized Boussinesq equation”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:4 (2017), 145–150

Citation in format AMSBIB
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\by V.~Z.~Furaev, A.~I.~Antonenko
\paper Approximation of solutions to the boundary value problems for the generalized Boussinesq equation
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 4
\pages 145--150
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\crossref{https://doi.org/10.14529/mmp170414}
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