Abstract
We develop a linearized compact alternating direction implicit (ADI) numerical method to solve the nonlinear delayed Schrödinger equation in two-dimensional space. By discrete energy estimate method, we analyse the convergence of the fully-discrete numerical method, and show that the numerical scheme is of order O(Δt2+h4) with time stepsize Δt and space stepsize h. At last, we present several numerical examples to confirm theoretical analyses.
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