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math.NA2010★ 20 cited
Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations
Philipp Bader, Sergio Blanes
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting…
math.NA2010★ 9 cited
Error analysis of splitting methods for the time dependent Schrodinger equation
Sergio Blanes, Fernando Casas, Ander Murua
A typical procedure to integrate numerically the time dependent Schrö\-din\-ger equation involves two stages. In the first one carries out a space discretization of the continuous…
math.NA2010
Splitting methods with complex coefficients
Sergio Blanes, Fernando Casas, Ander Murua
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by…