径向对称非线性Schrödinger方程的守恒差分格式

A CONSERVATIVE FINITE DIFFERENCE SCHEME FOR RADIAL SYMMETRIC NONLINEAR SCHRÖDINGER EQUATION

摘要: 对径向对称的非线性Schrödinger方程提出了一个新的守恒差分格式,这是一个三层格式,它不需迭代求解,因此提高了计算速度,同时也较好地保持了方程的两个守恒律。文中证明了格式的收敛性与稳定性,数值计算结果表明,该差分格式是有效的。

Abstract: A new finite difference scheme is proposed for radial symmetric nonlinear Schrödinger equation. This is a scheme of three levels which needn't to iterate. Thus, the new scheme requires less CPU time. Convergence and stability of the new scheme are proved. By means of numerical computation, it is followed that the new scheme is efficient.