Numerical Methods, Nonlinear Partial Differential Equations

The first chapter gives a new conservative finite difference scheme for generalized nonlinear Schr(o|¨)dinger equation. The difference scheme satisfies two conserved quantities and the scheme is stable and convergent.This chapter is devided into seven sections.The first section is introduction, which gives equationAnd two conserved quantitiesThe second chapter gives finite difference schemeAnd two conserved quantities of difference schemeIn the third section, we make an error estimate, which shows the scheme is convergent.