Journal of Advances in Applied Mathematics
Solution of the Neumann Problem with Respect to the Equation for Gravity-Gyroscopic Waves by the Finite Element Method
Download PDF (606.7 KB) PP. 107 - 119 Pub. Date: April 12, 2016
Author(s)
- Mykhail Moskalkov*
National Aviation University, Kyiv, Ukraine - Dauletbay Utebaev
Berdakh Kara-Kalpak State University, Nukus, Uzbekistan
Abstract
Keywords
References
[1] S.A. Gabov and A.G. Sveshnikov, Linear Problems in the Theory of Non-Steady-State Internal Waves, Nauka, Moscow, 1990.
[2] S.A. Gabov and Y.D. Pletner, "On an Initial Boundary Value Problem with Respect to the Equation for Gravity-Gyroscopic Waves," Journal of Computational Mathematics and Mathematical Physics, vol. 25, no.11, pp. 1689-1696, 1985.
[3] S.A. Gabov and Y.D. Pletner, "Equation for Gravity-Gyroscopic Waves: Annular Potential and its Application,” Journal of Computational Mathematics and Mathematical Physics, vol. 27, no. 1, pp. 102-113, 1997.
[4] G.B. Whitham, Linear and Nonlinear Waves. Wiley, Hoboken. 1974.
[5] Y.Z. Miropolskiy, Dynamics of Internal Waves in the Ocean, Gidrometeoizdat, Moscow, 1981.
[6] M.N. Moskalkov and D. Utebaev, "Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain," Applied Mathematics, vol. 5, no. 8, pp. 1120-1132, 2014. http://dx.doi.org/10.4236/am.2014.58105
[7] O.C. Zienkiewicz and K. Morgan, Finite Elements and Approximation, Wiley, Hoboken, 1983.
[8] O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, Butterworth-Heinemann, 2000.
[9] A.A. Samarskii, Theory of Difference Schemes, Nauka, Moskow, 1977.
[10] M.N. Moskalkov, "Scheme of the High-Accuracy Finite Element Method for Solving Non-Steady-State Second-Order Equations," Differential Equations, vol. 16, no. 7, pp. 1283-1292, 1980.
[11] M.N. Moskalkov and D. Utebaev, "Investigation of difference schemes of finite element method for second-order unsteady-state equations," Journal Computation Applied Mathematics, Kiev, no. 92, pp. 70 – 76. 2005.
[12] M.N. Moskalkov and D. Utebaev, "Comparison of Some Methods for Solving the Internal Wave Propagation Problem in a Weakly Stratified Fluid,” Mathematical Models and Computer Simulations. vol. 3, no. 2, pp. 264-271, 2012. http://dx.doi.org/10.1134/S2070048211020086
[13] M.N. Moskalkov and D. Utebaev, "Finite Element Method for the Gravity-Gyroscopic Wave Equation," Journal Computation and Applied Mathematics, no. 2(101), pp. 97 – 104, 2010.
[14] M.N. Moskalkov and D. Utebaev, "Convergence of the Finite Element Scheme for the Equation of Internal Waves," Cybernetics and Systems Analysis, vol. 47, no. 3, pp. 459-465. http://dx.doi.org/10.1007/s10559-011-9327-1
[15] A.N. Tikhonov and V.Y. Arsenin, Methods for Solving Incorrect Problems, Nauka, Moscow, 1986.