抛物型偏微分方程的新型差分格式

针对抛物型偏微分方程，通过给出数个新型差分格式，归纳出一种构造偏微方程新型差分格式的待定系数法：先列出统一的包含多个待定系数的新型差分格式，找出为使该格式稳定且满足相应的精度，系数应满足的一系列关系式。取满足上述关系式的各系数的不同组合值，可以很方便的构造出不同的新型差分格式。最后，把此方法推广到二阶抛物型方程，得到了数个绝对稳定的新型差分格式。方法简单实用，可应用于高阶抛物型方程以及其它类型偏微分方程的差分格式的构造，可以构造大量的差分格式，以满足不同的使用目的。

Study on new difference forms of partial differential equations

Taken parabolic partial differential equations (PDE) as the object of study, a method of awaiting determined coefficients was given out so that new difference forms of PDE were gained. Firstly new difference forms including several awaiting determined coefficients were presented. Then, a series of relationship equations correlated with awaiting determined coefficients can be obtained when new difference forms can be satisfied with stability and error control requirements. Several new difference forms could be made up conveniently so long as awaiting determined coefficients were equal to different combinatorial values. Finally, the method was spread into second order parabolic PDE, some new difference forms satifying absolute satibility conditions could be easily given out. The method may also be extended through to high order parabolic PDE and other kinds of PDE. It is a simpled and practical method, many difference forms could be found out so as to be suitable for different purposes.