An efficient local meshless method for the equal width equation in fluid mechanics

This paper proposes an accurate and robust meshless approach for the numerical solution of the nonlinear equal width equation. The numerical technique is applied for approximating the spatial variable derivatives of the model based on the localized radial basis function-finite difference (RBF-FD) method. Another implicit technique based on theta-weighted and finite difference methods is also employed for approximating the time variable derivatives. The stability analysis of the approach is demonstrated by employing the Von Neumann approach. Next, six test problems are solved including single solitary wave, fusion of two solitary waves, fusion of three solitary waves, soliton collision, undular bore, and the Maxwellian initial condition. Then, the L-2 and L-infinity, norm errors for the first example and the I-1, I-2, and I-3 invariants for the other examples are calculated to assess accuracy of the method. Finally, the validity, efficiency and accuracy of the method are compared with those of other techniques in the literature.

Automated summary

The paper presents an accurate and robust meshless approach for solving the nonlinear equal width equation, using localized radial basis function-finite difference method and implicit techniques. The stability analysis and comparison with other techniques are also conducted to assess the validity, efficiency, and accuracy of the method.