A reduction principle for singular perturbation problems

摘要

A reduction principle which greatly facilitates solving of the outer solution of singular perturbation problems is proposed in this paper. Unlike the traditional method, no additional variables are introduced and thus, no additional equations are generated while solving for the outer solution. The proposed method can be easily automated with symbolic mathematics packages and requires minimal preprocessing of the original equation. It is also shown in the paper that while the traditional method can give rise to erroneous solutions, the proposed method does not suffer from this disadvantage. Lastly, with the proposed method, a class of degenerate equations (according to the traditional method) can be shown to possess an outer solution expandable in the perturbation parameter.