圆域上2阶奇异变系数问题的一种有效的差分法

针对圆域上2阶奇异变系数问题,提出了一种基于降维格式的有限差分方法.首先,利用极坐标变换,将原问题转化为一系列等价的1维问题;其次,针对每一个1维问题,建立了适当的差分格式,并证明了相应的误差估计;最后,给出了一些数值例子,数值结果表明该算法是非常有效的.

The Efficient Finite Difference Method for Second Order Singular Variable Coefficient Problems in a Circular Domain

The finite difference method based on dimension reduction scheme is proposed for the second order singular variable coefficient problems in a circular domain.Firstly,the original problem is transformed into a series of equivalent one-dimensional problems by using polar coordinate transformation.Then for each one-dimensional problem,the appropriate difference scheme and corresponding error estimate are established.Finally,some numerical examples are given,and the numerical results show that the algorithm is very effective.