一类变系数抛物型自由边界问题数值算法研究

A Kind of Free Boundary Problem of Variable Coefficient Parabolic Equations

主要讨论一维一相的变系数抛物型偏微分方程的自由边界问题.利用坐标变换,将自由边界的移动前沿固定,然后通过多项式展开将自由边界问题转化成常微分方程组求解(前沿固定方法);通过扰动方法求得问题的近似解析解.通过解冰融化问题,将其与解析解相比较.

This paper studies a kind of one-dimensional ＆ one-phase free boundary problems of variable coefficient parabolic equations. By using to immobilize the moving front by front-fixing transformation, we can get an ordinary differential equations by Chebyshev polynomials. The approximate analytical solution is got by using perturbation method. The numerical solutions obtained by two methods with analytical solutions is also compared.