On a discrete‐time collocation method for the nonlinear Schrödinger equation with wave operator

We consider a discrete‐time orthogonal spline collocation scheme for solving Schrödinger equation with wave operator. The scheme is proposed recently by Wang et al. (J Comput Appl Math 235 (2011), 1993–2005) and is showed to have high‐order convergence rate when a parameter θ in the scheme is not less than $frac{1}{4}$. In this article, we show that the result can be extended to include $thetain(0,frac{1}{4})$ under an assumption. Numerical example is given to justify the theoretical result. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013