Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (1): 13-15.

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Derivation and application compact scheme of coupling of first and second derivative

LI Jia, LUO Jisheng   

  1. Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2012-01-01 Published:2012-01-01


李 佳,罗纪生   

  1. 天津大学 机械工程学院力学系,天津 300072

Abstract: In the numerical calculation, the differential equations which are coupling equations of the first and second derivative need to be solved. In order to solve this kind of equations with the compact scheme, the compact scheme of coupling of the first and second derivative is derived. Using this scheme, the differential equations are dispersed directly. By the specific examples, the conclusions are that the compact scheme has advantages and is used to solve the two-dimensional partial differential equations.

Key words: coupling of the first and second derivative, compact scheme, differential equations, numerical calculation

摘要: 在数值计算中可能遇到求解一阶导数和二阶导数耦合的微分方程,为了能用紧致差分格式进行计算,针对这样的方程,建立了考虑一阶、二阶导数耦合的紧致差分格式,利用这一方法可以直接对方程进行离散求解。通过具体算例,验证该类紧致差分格式的优越性,还将这类紧致差分格式运用到求解二维偏微分方程中。

关键词: 一阶、二阶导数耦合, 紧致差分格式, 微分方程, 数值计算