# Numerical Investigation of the Boussinesq - Love Mathematical Models on Geometrical Graphs

A.A. Zamyshlyaeva, A.V. LutThe article is devoted to the numerical investigation of the Boussinesq - Love mathematical models on geometrical graphs representing constructions made of thin elastic rods. The first paragraph describes the developed algorithm for numerical solution of the Boussinesq - Love equation with initial conditions and boundary conditions in the vertices. The block diagram of the algorithm is given and described. The result of computation experiment is given in the second paragraph.Full text

- Keywords
- geometrical graph; the Sobolev type model; the Sturm - Liouville problem; the Boussinesq - Love mathematical model.
- References
- 1. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity. Cambridge, At the University Press, 1927.

2. Uizem G. Linear and Nonlinear Waves. М., Mir, 1977.

3. Bayazitova A.A. The Sturm - Liouville Problem on Geometric Graph. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2010, no. 16 (192), issue 5, pp. 4-10. (in Russian)

4. Zamyshlyaeva A.A., Sviridyuk G.A. Nonclassical Equations of Mathematical Physics. Linear Sobolev Type Equations of Higher Order. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2016, vol. 8, no. 4, pp. 5-16. DOI: 10.14529/mmph160401

5. Zamyshlyaeva A.A. On Algorithm of Numerical Modelling of the Boussinesq - Love Waves. Bulletin of the South Ural State University. Series: Computer Technologies, Automatic Control and Radioelectronics, 2013, vol. 13, no. 4, pp. 24-29. (in Russian)

6. Zamyshlyaeva A.A., Surovtsev S.V. Finding of a Numerical Solution to the Cauchy - Dirichlet Problem for Boussinesq - Love Equation Using Finite Difference Method. Bulletin of the Samara State University. Natural Science Series, 2015, no. 6, pp. 76-81. (in Russian)

7. Zamyshlyaeva A.A., Lut A.V. Boussinesq - Love Mathematical Model on a Geometrical Graph. Journal of Computational and Engineering Mathematics, 2015, vol. 2, no. 2, pp. 82-97. DOI: 10.14529/jcem150208

8. Demidenko G.V., Uspenskii S.V. Partial Differential Equations and Systems not Solvable with Respect to the Highest Order Derivative. N.Y., Basel, Hong Kong, Marcel Dekker, 2003.

9. Showalter R.E. Hilbert Space Methods for Partial Differential Equations. London, Pitman Publ., 1977.

10. Al'shin A.B., Korpusov M.O., Sveshnikov A.G. Blow-up in Nonlinear Sobolev Type Equations. Berlin, N.Y., De Gruyter, 2011. DOI: 10.1515/9783110255294