一种用曲线坐标求边值问题数值解的方法

Method for solving free boundary problems via curve coordinate

给出了一种用曲线坐标求解椭圆型偏微分方程自由边值问题的数值解法；该方法通过引入两个辅助问题，它们构成一个曲线坐标系．在这个坐标系下，原问题化为矩形域上的方程组的固定边值问题．后者容易用差分法求解，其优点是简单省时．

A numerical method is proposed for solving free boundary problems of elliptic partial differential equations in terms of curve coordinates. A curve coordinate system is established in which the original problem may be reduced to a fixed boundary problem over a rectangular region and thus may be solved by difference methods. Three algorithmic examples are given to demonstrate the method.