Z. Naturforsch. **68a,** 547 – 553
(2013)

doi:10.5560/ZNA.2013-0036

A Numerical Study for the Solution of Time Fractional Nonlinear Shallow Water Equation in Oceans

Sunil
Kumar

Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India

Received January 11, 2013 / revised March 17, 2013 / published online June 12, 2013

In this paper, an analytical solution for the coupled one-dimensional time fractional nonlinear shallow water system is obtained by using the homotopy perturbation method (HPM). The shallow water equations are a system of partial differential equations governing fluid flow in the oceans (sometimes), coastal regions (usually), estuaries (almost always), rivers and channels (almost always). The general characteristic of shallow water flows is that the vertical dimension is much smaller than the typical horizontal scale. This method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. A very satisfactory approximate solution of the system with accuracy of the order 10^{−4} is obtained by truncating the HPM solution series at level six.

*Key words:* Nonlinear Shallow Water System; Approximate Analytical Solution; Homotopy Perturbation Method; Caputo Derivatives.