ERROR ESTIMATE OF FOURTH-ORDER COMPACT SCHEME FOR LINEAR SCHRODINGER EQUATIONS

作者：Liao, Hong-lin^*; Sun, Zhi-zhong; Shi, Han-sheng

来源：SIAM Journal on Numerical Analysis, 2010, 47(6): 4381-4401.

DOI：10.1137/080714907

• linear Schrodinger equation
• fourth-order compact scheme
• discrete energy analysis
• maximum norm error estimate
• asymptotic expansion

A fourth-order compact difference scheme is proposed for two-dimensional linear Schrodinger equations with periodic boundary conditions. By using the discrete energy method, it is proven that the difference scheme is uniquely solvable, unconditionally stable, and convergent. A maximum norm error estimate and thus an asymptotic expansion of the discrete solution are also obtained. Using the expansion of the difference solution, high-order approximations could be achieved by Richardson extrapolations. Extension to three-dimensional problems is also discussed. Numerical experiments are included to support the theoretical results, and comparisons with the Crank-Nicolson method are presented to show the effectiveness of our method.

• 出版日期2010
• 单位东南大学