Geodesic
Numerical Study of Traveling Wave Solutions to 2D Boussinesq Equation
Serdica Journal of Computing, Tome 13 (2019) no. 1-2, pp. 001-016
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The aim of this paper is to evaluate stationary propagating wave solutions to the two dimensional Boussinesq equation. To solve the resulting nonlinear fourth order elliptic problem we use a combination of high order finite difference schemes, an iterative procedure and new asymptotic boundary conditions. A number of numerical results are obtained for the validation of the method and for the dependence of the wave's shape on the velocity c and dispersion parameters. We also give a comparison with the numerical results and best-fit formulae given in [4, 5].
Keywords: Two Dimensional Boussinesq Equation, Traveling Wave Solutions (TWS), High Order Finite Dierence Schemes, Asymptotic Boundary Conditions 
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     author = {Angelow, Krassimir and Kolkovska, Natalia},
     title = {Numerical {Study} of {Traveling} {Wave} {Solutions} to {2D} {Boussinesq} {Equation}},
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Angelow, Krassimir; Kolkovska, Natalia. Numerical Study of Traveling Wave Solutions to 2D Boussinesq Equation. Serdica Journal of Computing, Tome 13 (2019) no. 1-2, pp. 001-016. http://geodesic.mathdoc.fr/item/SJC_2019_13_1-2_a0/