High-accuracy Algorithms For One Dimensional Singular Interface Problems

This thesis presents a numerical method for one dimensional interface problems with a singular variable coefficient that has a finite jump across the interface.The key of the idea includes the following three parts.First the interface problem can be fully decoupled as two-point boundary value problems with undetermined param-eters.Then on the sub-interval near the interface point,we propose an algorithm of Puiseux expansions based on Adomian decomposition method to solve the two decou-pled problems separately.And,for the remaining interval,compact finite difference method is presented to solve the regular boundary value problem.Finally,some nu-merical examples are presented to show the high-accuracy solution and the efficiency of our method.