A localized meshfree technique for solving fractional Benjamin–Ono equation describing long internal waves in deep stratified fluids

Abstract

This article proposes a local radial basis function partition of unity method to find the numerical solution of the time-fractional Benjamin–Ono equation. The proposed method is based on partitioning the original domain into several overlapping subdomains and employing the radial basis function approximation on each local subdomain. First, the time-discrete scheme of this equation is obtained by utilizing a finite difference approach. Then, spatial discretization is established by using the local radial basis function partition of unity method. Furthermore, the convergence and stability analysis of the proposed time-discrete scheme are investigated thoroughly. Also, numerical experiments are executed through some illustrated problems, and the results are compared with those acquired by the tanh approach and Kudryashov approach solutions to show the high accuracy and plausibility of the proposed method. Moreover, to demonstrate the physical significance, the conservation constants known as mass, momentum, and energy for this equation are also calculated by the proposed method.