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.
作者
刘博
陶善聪
时晓天
Liu Bo;Tao Shancong;Shi Xiaotian(China Academy of Aerospace Aerodynamics,Beijing 100074,China)
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.
关键词
抛物型方程
高精度
有限差分
加权系数
显隐格式
parabolic partial differential equation
high-resolution
finite difference scheme
weigh ted coefficients
explicit and implicit schemes
