A numerical approach for 2D time-fractional diffusion damped wave model

Abstract

In this article, we introduce an approximation of the rotated five-point difference Crank-Nicolson R(FPCN) approach for treating the second-order two-dimensional (2D) time-fractional diffusion-wave equation (TFDWE) with damping, which is constructed from two separate sets of equations, namely transverse electric and transverse magnetic phases. Such a category of equations can be achieved by altering second-order time derivative in the ordinary diffusion damped wave model by fractional Caputo derivative of order α while 1<α<2. The suggested methodology is developed from the standard five-points difference Crank-Nicolson S(FPCN) scheme by rotating clockwise 45o with respect to the standard knots. Numerical analysis is presented to demonstrate the applicability and feasibility of the R(FPCN) formulation over the S(FPCN) technique. The stability and convergence of the presented methodology are also performed.

Keywords

• fractional derivative
• standard and rotated five-point crank-nicolson approximations
• fractional diffusion damped wave model