A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients |
| |
Authors: | Mehdi Dehghan Ameneh Taleei |
| |
Affiliation: | Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914 Tehran, Iran |
| |
Abstract: | We propose a compact split-step finite difference method to solve the nonlinear Schrödinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and Gross-Pitaevskii equation. |
| |
Keywords: | Nonlinear Schrö dinger equation (NLS) Gross-Pitaevskii equation (GP) Operator splitting Compact split-step finite difference method (SSFD) |
本文献已被 ScienceDirect 等数据库收录! |