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This paper studies a finite difference method for one-dimensional nonhomogeneous Burgers' equation on the infinite domain. Two exact nonlinear artificial boundary conditions are applied on two artificial boundaries to limit the original problem onto a bounded computational domain. A function transformation makes both Burgers' equation and artificial boundary conditions linear. Consequently, a novel finite difference scheme is developed by using the method of reduction of order for the obtained equation and artificial boundary conditions. The stability and the convergence with order 3/2 in time and 2 in space in an energy norm are proved for this method for Burgers' equation. Different examples illustrate the unconditional stability and the accuracy of the proposed method.
Journal: Applied Numerical Mathematics - Volume 111, January 2017, Pages 1–16