摘要
自然科学及社会科学发展使人们对各类复杂系统研究逐渐深入,高阶波动积分方程在材料科学、力学及电磁学等诸多领域得到成功运用。波动积分方程优势明显,其数值解尤为重要,文中提出对高阶波动积分方程整体解存在性进行研究。运用有限差分法及sinc配置逼近高阶波动方程初边值数值解,先采用有限差分法在时间方向区域上对原问题实行半离散化处理,同时在空间方向区域上运用sinc配置法获得全离散格式,将原问题转换为求线性代数方程数值解,初步分析了波动积分方程边值问题。基于方程边值数值解存在性分析,采用标准压缩映像原理对方程局部解存在性先进行分析,通过能量积分法及连续性技术获得方程整体解,同时运用边界层强度的小性控制方程数值解稳定性。
The development of natural science and social sciences has made people gradually study the various complex systems, and the high order wave integral equations have been successfully applied in many fields, such as material science, mechanics and electromagnetics. The wave integral equation has obvious advantages, and its numerical solution is especially important. In this paper, the existence of global solutions for higher order wave integral equations is studied. By using the finite difference method and sinc collocation approximation numerical solution of the boundary value of high order wave equation, using finite difference method in time domain for the implementation of the original direction of semi discretization, while the use of sinc configuration method in spatial direction of regional get fully discrete format, the original problem can be transformed into linear algebraic equations the numerical solution, a preliminary analysis of the fluctuation of the integral equation boundary value problem. Numerical analysis of the existence of boundary value equations based on the principle of image compression, using the standard of the existence of local solutions to analyze the equation by the energy integral method and technique to obtain the overall continuity equation, small control equations and boundary layer stability using strength.
出处
《科技通报》
2018年第10期20-23,共4页
Bulletin of Science and Technology
基金
2017年度河南省政府决策研究招标课题(编号2017B056)
关键词
波动方程
有限差分法
整体解
能量积分
finite element
elliptic
partial differential equation
numerical solution
