一种解抛物型方程的三层九点高精度加权差分格式  

A NOVEL LEVEL 3-POINTS 9 HIGH RESOLUTION WEIGHTED FINITE DIFFERENCE SCHEME FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

作　　者：刘博 陶善聪 时晓天[1] Liu Bo;Tao Shancong;Shi Xiaotian(China Academy of Aerospace Aerodynamics,Beijing 100074,China)

机构地区：[1]中国航天空气动力技术研究院,北京100074

出　　处：《数值计算与计算机应用》2022年第2期163-175,共13页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金支持(11872348);国家重点研发计划(2019YFA040300)资助.

摘　　要：针对一维齐次常系数抛物型方程,采用显隐格式加权.构造出一种在时间和空间上分别达到四阶和八阶的高精度差分格式,通过理论推导,给出了满足稳定性条件的网比取值范围.通过数值实验及与文献方法的对比,验证了本文格式在满足稳定性的基础上可以达到预期的理论精度。A novel high resolution finite difference scheme based on weighted explicit and implicit scheme for one-dimensional homogeneous parabolic partial differential equation is configured in this paper.The scheme has 4th order in time and 8th order accuracy in space as can be seen from the theoretical analysis,the range of time-space grid ratio which satisfies the stability condition is also given in the present work.With numerical experiments and comparison with references,the theoretical accuracy of the current scheme is achieved.

关 键 词：抛物型方程 高精度 有限差分 加权系数 显隐格式 

分 类 号：O241.82[理学—计算数学]