Numerical analysis with a class of trigonometric functions for nonlinear time fractional Wu-Zhang system

Abstract

We study the implementation of a numerical method to solve the time fractional (2+1)-dimensional Wu–Zhang system focusing on properties of trigonometric basis functions (TBFs). The approximation of the system describing dispersive long waves by appropriate discretization of the system and Grünwald difference operators is discussed and a linear system of the resulting discrete systems is given. This process includes a presentation of a general framework to approximate the solution by a mesh-free scheme which is stable and converges. Finally, various numerical experiments are present to illustrate the exceptional effect of fractional-order on the WZ system.

Keywords

• Wu–Zhang system
• Non-linear equations
• Dispersion
• Surface velocity