Randomized trial analyzes discretization of cubic Schrödinger equation, discussing modified linearization techniques.
We analyze the discretization of an initial-boundary value problem for the cubic Schrödinger equation in one space dimension by a Crank-Nicolson-type finite difference scheme. We then linearize the corresponding equations at each time level by Newton's method and discuss an iterative modification of the linearized scheme which requires solving linear systems with the same tridiagonal matrix. We prove second-order error estimates.
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Georgios Akrivis (1993) studied this question.
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