一维非线性 Schrödinger 方程参数形式差分格式的研究

摘要

对一维非线性 Schrdinger 方程构造参数形式的差分格式进行研究。运用能量方法证明了方程的离散守恒律，并通过先验估计验证了格式的收敛性和稳定性。数值实验结果表明，差分格式的收敛阶为 O（h 2＋τ2），格式的效果明显优于先前格式。%A parameter finite difference scheme is proposed for nonlinear Schrdinger equation in one dimension. Then the discrete conservation law is proved by the energy method.The stability and convergence are demonstrated by the prior estimation.The numerical results have been carried out to confirm the convergence order is O(h 2 +τ2 ). Moreover,the new scheme shows the superiority through comparing with the scheme before.