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

作　　者：崔进[1] 吴宏伟[2] 

机构地区：[1]南京信息职业技术学院基础部,江苏南京210023 [2]东南大学数学系,江苏南京210096

出　　处：《应用数学》2014年第1期166-174,共9页Mathematica Applicata

基　　金：国家自然科学基金项目(11271068)

摘　　要：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.

关 键 词：波动方程 高阶 隐格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]