一类波动方程初边值问题的高阶差分格式

A High Order Difference Scheme for the Solution of Wave Equation with Initial-boundary Value Problem

本文研究波动方程初边值问题的高精度差分方法,首先提出一个高阶隐式差分格式,然后通过能量方法证明先验估计式,从而得到差分解的无条件收敛性和稳定性,最后通过数值算例验证了理论分析,差分解在L∞下收敛阶数为O(τ2+h4).

The article is devoted to a new high accurate method for wave equation with initial-boundary value. First, a high order implicit difference scheme is derived. Then,a priori estimate for the difference scheme is shown by the energy analysis method. The convergence and stability are obtained by the priori estimate. Finally, some numerical experiments are presented to verify the theoretical analysis. The convergence order is O（τ^2＋h^4） in the discrete L∞ norm.