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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.