一阶、二阶导数耦合的紧致差分格式及其应用

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

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。

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.