  In this paper, we propose a new adaptation of the D-iteration algorithm to
numerically solve the differential equations. This problem can be reinterpreted
in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the
boundary or initial conditions are replaced by fluid catalysts. Pre-computing
the diffusion process for an elementary catalyst case as a fundamental block of
a class of differential equations, we show that the computation efficiency can
be greatly improved. The method can be applied on the class of problems that
can be addressed by the Gauss-Seidel iteration, based on the linear
approximation of the differential equations.
