SIAM Journal on Numerical Analysis · 2002 · 164 citations · 15 references
Numerical AnalysisEngineeringResolvent KernelSplitting MethodsRiemann-hilbert ProblemNonlinear Wave PropagationExact SolutionStrang FormulaeNonlinear EquationNonlinear Hyperbolic ProblemFunctional AnalysisIntegrable SystemNonlinear Schrödinger EquationOrder EstimatesNonlinear Functional Analysis
In this paper, we consider the nonlinear Schrödinger equation $u_t+i\Delta u -F(u)=0$ in two dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang formulae (which are splitting methods) are approximations of the exact solution of order 1 and 2 in time.
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On the Construction and Comparison of Difference Schemes
Gilbert Strang · SIAM Journal on Numerical Analysis · 1968 · 3.4K citations
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