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Computational study of some nonlinear shallow water equations

100%

Bhrawy A., Abdelkawy M.

Open Physics

2013

vol. 11

issue 4

518-525

The shallow water equations have wide applications in ocean, atmospheric modeling and hydraulic engineering, also they can be used to model flows in rivers and coastal areas. In this article we obtained exact solutions of three equations of shallow water by using $\frac{{G'}} {G} $-expansion method. Hyperbolic and triangular periodic solutions can be obtained from the $\frac{{G'}} {G} $-expansion method.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

81%

Doha E., Bhrawy A., Abdelkawy M., Hafez R.

Open Physics

2014

vol. 12

issue 2

111-122

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers’ equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers’ equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

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2 Open Physics

1 2014

1 2013

2 Abdelkawy M.

2 Bhrawy A.

1 Doha E.

1 Hafez R.

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Computational study of some nonlinear shallow water equations

A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation