有相变的变系数抛物型微分方程自由边界问题

A free boundary problem of parabolic equation with variable coefficient under the existence of phase-change

研究一类变系数抛物型微分方程的自由边界问题,根据变系数这一特点,用积分插值法建立方程的守恒差分格式。在方程有相变的情况下,相应地用显式差分格式逼近微分方程,得到离散点温度值随时间或空间变量变化的规律。

A free boundary problem of parabolic equation with variable coefficients is mainly investigated in this paper. In view of the variable coefficients, the conservation difference scheme of the equation is de- rived through the integral interpolation method. Under the condition of existence of phase-change, the ex- plicit difference scheme to approximate the differential equation is given; the changing laws of the tempera- ture at discrete point varying with the time and space variables are obtained.