Local absorbing boundary conditions for a linearized Korteweg-de Vries equation.

Abstract

The aim of this paper is to construct highly accurate local absorbing boundary conditions for a linearized Korteweg-de Vries equation on unbounded domain. The local absorbing boundary conditions are derived by Padé approximation with high accuracy, and a sequence of auxiliary variables are utilized to avoid the high-order derivatives in the absorbing boundary conditions. Then the original problem on unbounded domain is replaced by an equivalent initial boundary value problem defined on a finite domain. The finite difference method is applied to solve the reduced problem on the finite computational domain. Finally, numerical results are presented to demonstrate the effectiveness and accuracy of the proposed method.