International Conference on Computational Methods in Applied Sciences, İstanbul, Turkey, 12  16 July 2019, pp.202203
In this study, we consider the following coupled system of Burgers’
equations with timefractional 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 timefractional 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 timefractional derivative.
In this study, we consider the following coupled system of Burgers’
equations with timefractional 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 timefractional 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 timefractional derivative.