Dynamic programming solutions of mildly non-linear elliptic problems over irregular regions

Abstract

A numerical method for solving midly non-linear elliptic problems over irregular regions is proposed in the paper. The given irregular region is imbedded in a region of simple geometry. The original non-linear problem is replaced by a sequence of linear problems by using the technique of quasi-linearisation. The method of dynamic programming is then used for computing the required solutions. The method is illustrated by solving a given problem. It is found that the proposed method is fast and can be applied to problems over complex regions.