## Numerical Approaches for solving the Coupled System of Burgers’ Equations with Time-Fractional Derivative using Gegenbauer wavelets

International Conference on Computational Methods in Applied Sciences, İstanbul, Turkey, 12 - 16 July 2019, pp.202-203

• Publication Type: Conference Paper / Full Text
• City: İstanbul
• Country: Turkey
• Page Numbers: pp.202-203
• Yıldız Technical University Affiliated: Yes

#### Abstract

In this study, we consider the following coupled system of Burgers’ equations with time-fractional derivative:

with initial and boundary conditions

and

in which  parameter depicts the order of time fractional derivatives.  and  are arbitrary constants hinging on the system such as the Peclet number, Stokes velocity of particles due to gravity, and Brownian diffusivity. and  are the velocity components,  is the nonlinear convection term,  is the diffusion term .

Our aim is to develop the Gegenbauer wavelet collocation method and the Gegenbauer wavelet Galerkin method for numerical solution of the problem. These methods are combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of  the coupled system of Burgers’ equations with time-fractional derivative. At the end of the study, it is shown that these methods are powerful tools for solving the coupled system of Burgers’ equations with time-fractional derivative.

In this study, we consider the following coupled system of Burgers’ equations with time-fractional derivative:

with initial and boundary conditions

and

in which  parameter depicts the order of time fractional derivatives.  and  are arbitrary constants hinging on the system such as the Peclet number, Stokes velocity of particles due to gravity, and Brownian diffusivity. and  are the velocity components,  is the nonlinear convection term,  is the diffusion term .

Our aim is to develop the Gegenbauer wavelet collocation method and the Gegenbauer wavelet Galerkin method for numerical solution of the problem. These methods are combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of  the coupled system of Burgers’ equations with time-fractional derivative. At the end of the study, it is shown that these methods are powerful tools for solving the coupled system of Burgers’ equations with time-fractional derivative.