Numerical Approximation of Fractional Burgers Equation

Abstract

The mathematical modeling of physical and chemical systems is used extensively throughout science, engineering and applied mathematics. In order to make use of mathematical models, it is necessary to have solutions to the model equations. Generally, this requires numerical methods because of the complexity and number of equations. In this paper, we study and approximate a nonlinear fractional Burgers problem by finite volume schemes of order one in space and also in time. The purpose is to show that they converge to the solution of the considered problem and to establish error estimates. We prove that the finite volume schemes converge to weak entropic solutions as the discretization parameters tend to zero.