摘要
针对一类二阶线性波动方程,首先根据时空紧算子构造了一类新的紧差分格式,证明了差分格式解的存在性和唯一性;其次,利用Fourier分析法得到建立的紧差分格式的条件稳定性;再次,利用Lax定理和相容性条件证明数值格式的收敛性,收敛阶在L~∞范数下为O(τ~4+h^4)。数值计算的结果验证了理论结果。
Firstly, for a class of second order linear wave equations, a class of new compact difference scheme was constructed according to space-time compact operator and the unique solvability was proved. Secondly, the conditional stability of the scheme was gained by using Fourier analysis. Thirdly, the convergence of numerical format was proven by Lax-Milgram theorem and compatibility condition and the convergence order was O(τ~4+h^4) in L~∞ norm. Numerical calculation result testified the theoretical results.
作者
林晓嫚
张启峰
徐映红
LIN Xiaoman;ZHANG Qifeng;XU Yinghong((School of Sciences,Zhejiang Sci-Tech University,Hangzhou 310018,China)
出处
《浙江理工大学学报（自然科学版）》
2019年第2期249-254,共6页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
基金
浙江省自然科学基金项目(Y19A010080)
国家自然科学基金项目(11541514
11501513)
关键词
波动方程
紧差分格式
可解性
收敛性
稳定性
wave equations
compact difference scheme
solvability
convergence
stability
