一类椭圆型变系数方程的差分格式

A Finite Difference Scheme for A Class of Elliptic Differential Equation with Variable Coefficients

研究了一类二阶椭圆型变系数方程的初边值问题的求解方法,建立了一种差分格式,并且运用能量方法证明了这种格式的解的存在唯一性、收敛性和稳定性,所得结果是对相关文献中结果的一个补充。

The initial boundary value problem of a second order elliptic differential equation with variable coefficients is studied. A finite difference scheme is established, and the existence, convergence and stability of this difference scheme is analysised with the apply of the energy method,the result obtained can serve as a complement to the known results in related literatures.