A Leap Frog Finite Difference Scheme for a Class of Nonlinear Schrödinger Equations of High Order (Journal of Computational Mathematics, 1999)
In this paper, the periodic initial value problem for the following class of nonlinear schr\u00f6dinger equation of high order $$i\u00a0\frac{\u2202u}{\u2202t} + (\u20131)^m \frac{\u2202^m}{\u2202x^m} \Bigg( a(x) \frac{\u2202^mu}{\u2202x^m} \Bigg) +\u00a0\u03b2\f(x)q(|u|^2)u + f (x; t)u = g(x; t)$$ is considered. A leap-frog finite difference scheme is given, and convergence and stability is proved. Finally, it is shown by a numerical example that numerical result is coincident with theoretical result.\u00a0
Keywords: High order nonlinear Schrödinger equation; Leap-Frog difference scheme; Convergence.