A finite difference method for Burgers' equation in the unbounded domain using artificial boundary conditions

This paper discusses the numerical solution of one-dimensional Burgers' equation in the infinite domain. The original problem is converted by Hopf-Cole transformation to the heat equation in the infinite domain, the latter is reduced to an equivalent problem in a finite computational domain with two artificial integral boundary conditions, a finite difference method is constructed for last problem by the method of reduction of order, and therefore the numerical solution of Burgers' equation is obtained. The method is proved and verified to be uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time for solving the heat equation as well as Burgers' equation in the computational domain.