Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, there is a striking manifestation of support splitting and merging phenomena in the behaviour of non-stationary seepage. The model equation in one dimensional space is written in the form of the initial-boundary value problem with the effect of a non-linear filtration. In this paper, such phenomena are realized by use of finite difference schemes, and are justified from numerical and analytical points of view.