The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving kriging interpolation shape functions with the weighted essentially non-oscillatory method

In this investigation a new meshless numerical technique is proposed for solving Green-Naghdi equation by combining the moving Kriging interpolation shape functions with the weighted essentially non-oscillatory (WENO) method. The present approach has been taken from [12, 30]. The convergence order of WENO technique can be studied by the number of interpolation nodes because this method is described by interpolation concept. The proposed method is based on the non-polynomial WENO procedure in order to increase the convergence order and local accuracy. Four examples have been solved that they show the efficiency and accuracy of the proposed method.