Fractional Porous Medium Equations to Non-Darcian Flow by Means of the Bernstein Polynomials

Abstract

The Bernstein polynomials is used to develop the fractional differential Swartzendruber model in porous media. With the operator matrix of the Bernstein polynomials, the fractional differential Swartzendruber equation is transformed into the products of several dependent matrixs which can also be regarded as the system of linear equations after dispersing the variable. By solving the system of linear equations, the numerical solutions are acquired. Some experimental data are provided to show that the method is computationally efficient and accurate.