Stability analysis of local artificial boundary conditions for some time dependent nonlinear partial differential equations

This project is about the stability analysis of local artificial boundary conditons for some nonlinear partial differential equations on unbounded domains. Artificial boundaries are introduced to seperate the unbounded domains, and local boundary conditions will be obtained on the artificial boundaries, which are in nonlinear forms. Then, the original problems are reduced to initial boundary value problems on bounded computational domains. The main task of this project is the stability analysis. We will first consider the one dimensional Schrodinger equation with a general nonlinear potential, perform the numerical tests for stability and stability analysis, and then consider the two dimensional Schrodinger equation with a general nonlinear potential. Finally, we will discuss the atability of local artificial boundary conditons for some other related problems.