**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31181

##### An Application of the Sinc-Collocation Method to a Three-Dimensional Oceanography Model

**Authors:**
Y. Mohseniahouei,
K. Abdella,
M. Pollanen

**Abstract:**

**Keywords:**
Differential Equations,
Boundary Value Problems,
Wind-Driven Currents,
Sinc Numerical Methods

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1331273

**References:**

[1] M. A. Noor and E. Al-Said, "Finite-difference method for a system of third-order boundary-value problems," Journal of optimization theory and applications, vol. 112, no. 3, pp. 627-637, 2002.

[2] O. Axelsson and V. A. Barker, Finite element solution of boundary value problems: theory and computation. Society for Industrial and Applied Mathematics, 1987, vol. 35.

[3] Z. Csendes, "A novel finite element method for two-point boundary value problems," Mathematics and Computers in Simulation, vol. 20, no. 3, pp. 197-203, 1978.

[4] K. Ruotsalainen and W. Wendland, "On the boundary element method for some nonlinear boundary value problems," Numerische Mathematik, vol. 53, no. 3, pp. 299-314, 1988.

[5] B. S. Attili and M. I. Syam, "Efficient shooting method for solving two point boundary value problems," Chaos, Solitons & Fractals, vol. 35, no. 5, pp. 895-903, 2008.

[6] J. Rashidinia and M. Ghasemi, "B-spline collocation for solution of twopoint boundary value problems," Journal of computational and applied mathematics, vol. 235, no. 8, pp. 2325-2342, 2011.

[7] F. Stenger, "Summary of sinc numerical methods," Journal of Computational and Applied Mathematics, vol. 121, no. 1, pp. 379-420, 2000.

[8] F. Keinert, "Uniform approximation to x β by sinc functions," Journal of approximation theory, vol. 66, no. 1, pp. 44-52, 1991.

[9] S. Narasimhan, J. Majdalani, and F. Stenger, "A first step in applying the sinc collocation method to the nonlinear navier-stokes equations," Numerical Heat Transfer: Part B: Fundamentals, vol. 41, no. 5, pp. 447-462, 2002.

[10] A. Lippke, "Analytical solutions and sinc function approximations in thermal conduction with nonlinear heat generation," Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C);(United States), vol. 113, no. 1, 1991.

[11] K. Al-Khaled, "Numerical approximations for population growth models," Applied mathematics and computation, vol. 160, no. 3, pp. 865-873, 2005.

[12] J. Lund and C. R. Vogel, "A fully-galerkin method for the numerical solution of an inverse problem in a parabolic partial differential equation," Inverse Problems, vol. 6, no. 2, p. 205, 1999.

[13] R. C. Smith and K. L. Bowers, "Sinc-galerkin estimation of diffusivity in parabolic problems," Inverse problems, vol. 9, no. 1, p. 113, 1999.

[14] K. Parand and A. Pirkhedri, "Sinc-collocation method for solving astrophysics equations," New Astronomy, vol. 15, no. 6, pp. 533-537, 2010.

[15] M. El-Gamel and A. Zayed, "Sinc-galerkin method for solving nonlinear boundary-value problems," Computers & Mathematics with Applications, vol. 48, no. 9, pp. 1285-1298, 2004.

[16] F. Stenger and M. J. O-Reilly, "Computing solutions to medical problems via sinc convolution," Automatic Control, IEEE Transactions on, vol. 43, no. 6, pp. 843-848, 1998.

[17] K. Abdella, X. Yu, and I. Kucuk, "Application of the sinc method to a dynamic elasto-plastic problem," Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 626-645, 2009.

[18] D. Winter, K. L. Bowers, and J. Lund, "Wind-driven currents in a sea with a variable eddy viscosity calculated via a sinc-galerkin technique," International journal for numerical methods in fluids, vol. 33, no. 7, pp. 1041-1073, 2000.

[19] S. Koonprasert and K. L. Bowers, "Block matrix sinc-galerkin solution of the wind-driven current problem," Applied mathematics and computation, vol. 155, no. 3, pp. 607-635, 2004.

[20] E. Hesameddini and E. Asadolahifard, "The sinc-collocation method for solving the telegraph equation," Journal of Computer Engineering and Informatics.

[21] A. Saadatmandi, "Numerical study of second painlev'e equation," Communications in Numerical Analysis, vol. 2012, 2012.

[22] B. Bialecki, "Sinc-collection methods for two-point boundary value problems," IMA Journal of Numerical Analysis, vol. 11, no. 3, pp. 357- 375, 1991.

[23] V. W. Ekman, "On the influence of the earth\-s rotation on ocean currents," Ark. Mat. Astron. Fys., vol. 2, pp. 1-53, 1905.

[24] N. Heaps et al., "On the numerical solution of the three-dimensional hydrodynamical equations for tides and storm surges," M'emoires de la Soci'et'e Royale des Sciences de Li`ege. Sixi`eme S'erie, 1972.

[25] N. Heaps, "Three-dimensional model for tides and surges with vertical eddy viscosity prescribed in two layersi. mathematical formulation," Geophysical Journal of the Royal Astronomical Society, vol. 64, no. 1, pp. 291-302, 1981.

[26] R. Lardner and Y. Song, "A hybrid spectral method for the threedimensional numerical modelling of nonlinear flows in shallow seas," Journal of Computational Physics, vol. 100, no. 2, pp. 322-334, 1992.

[27] A. Davies, "The numerical solution of the three-dimensional hydrodynamic equations, using a b-spline representation of the vertical current profile," Elsevier Oceanography Series, vol. 19, pp. 1-25, 1977.

[28] A. Davies and A. Owen, "Three dimensional numerical sea model using the galerkin method with a polynomial basis set," Applied mathematical modelling, vol. 3, no. 6, pp. 421-428, 1979.

[29] A. M. Davies, "Solution of the 3d linear hydrodynamic equations using an enhanced eigenfunction approach," International journal for numerical methods in fluids, vol. 13, no. 2, pp. 235-250, 1991.

[30] K. Abdella, "Numerical solution of two-point boundary value problems using sinc interpolation," in Proceedings of the American Conference on Applied Mathematics (American-Math-12): Applied Mathematics in Electrical and Computer Engineering, 2012, pp. 157-162.

[31] R. Burden and J. Faires, "Numerical analysis 7th ed., brooks/cole, thomson learning," 2001.

[32] S. Koonprasert, "The sinc-galerkin method for problems," Ph.D. dissertation, MONTANA STATE UNIVERSITY Bozeman, 2003.