In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms of the equation derived using standard length or area measure on a discrete approximation of the fractal set. We then introduce a numerical procedure to normalize the obtained diffusions, that is, a way to compute the renormalization constant needed in the definitions of the actual partial differential equation on the fractal set. A particular case that is studied in detail is the solution of the Dirichlet problem in the Sierpinski triangle. Other examples are also presented including a non-planar Hata tree.

翻译：在本文中,我们提出计算分形上部分差异方程式的解决方案的数字程序,特别是,我们用标准图形 Laplacian 矩阵和以标准长度或面积测量法得出的分形集离散近似标准方程式的薄弱方程式来考虑方程式的强烈形式,然后我们引入一个数字程序,使获得的散射标准化,即一种计算分形上实际部分差异方程式定义中所需的重新整形常数的方法,一个具体的案例是Sierpinski三角体Drichlet问题的解决方案,其他的例子包括非平面的Hata树。