Compact Difference Scheme For Solving The Nonlinear Schrodinger Equation Involving Quintic Term

Based on the finite difference method, two compact finite difference schemes are given to solve the nonlinear Schr?dinger equation involving quintic term. The first scheme is a two level nonlinear scheme. An iterative algorithm should be used to obtain the numerical solution. In theory, the unconditional stability and convergence in maximum norm are proved by the energy method. The result of the theory is confirmed by the numerical experiment. The efficiency of the scheme is proved compared with the one in previous paper. The second scheme in this paper is a three level nonlinear scheme. The convergence and the unconditional stability are confirmed in theory and numerical experiment. The conservation of the mass can be proved and the precision of this scheme is also)(42?hO ?. At last, we compare the two difference schemes in maximum norm and computing time.