A novel approach to Burgers' equation

Abstract

SUMMARYA new method is presented for the numerical solution of Burgers' equation. In this method, the Green's function of the linear heat conduction equation is employed to convert Burgers' equation to the corresponding integration equation system with respect to the time variable. Then the solution of this integration system is obtained by a numerical method. The computed results show that this method can deal with a wide range of Reynolds number and in the moderate Reynolds number case, even with the comparatively larger time step, good accuracy can be achieved. Furthermore, this method does not require spatial discretization.

Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations

“…Since then, it has been the original model describing interaction of convection and dissipation-flow. In fact, Burgers equation has always been an important equation of fluid dynamics for half a century, and even till now its analytical and numerical solutions are still a subject of study [3][4][5][6][7][8] .…”

On the inverse problem for one-dimensional Burgers' equation from the interior observation

“…Burgers' equation arises from many areas of applied mathematics such as fluid mechanics, traffic flow, gas dynamics [2,8,12]. Due to huge applications, this equation attracted a lot of mathematicians to study both for the forward problems as well as the inverse ones [1,2,4,15]. The existence and the properties of the solutions to forward problem of Burgers' equation have considered [5,11,16].…”

Numerical solutions of Burgers' equation in a B-polynomial basis

“…This requires an enormous number of grid points to correctly describe the numerical solution in that region. More recently, Xu and Duan [14] used a Green's function approach which only requires discretization of the time variable, while the spatial part of the solution retains the analytic form and shows very good accuracy for Burgers' equation with moderate Reynolds number.…”