Abstract: Some representative examples are adopted in this paper to discuss the differences between the stability conditions deduced from the original partial differential equations and that obtained from the expansion equations. It shows that for some difference equations, we’d better adopt the expansion equations in the process of the heuristic method being applied to these difference equations. In another part, apagoge is used in this paper to tell us that not all the stability conditions deduced by the heuristic method are the necessary computational stability conditions, which should be pay attention to in their applications.

Key words: heuristic method, finite-difference equation, computational stability