Order estimates in time of splitting methods for the nonlinear Schrödinger equation
Jan 1, 2002·
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Christophe Besse
Brigitte Bidégaray
Stéphane Descombes
Initial data for the numerical experiments
Abstract
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.
Type
Publication
SIAM Journal on Numerical Analysis, 40(1), 26–40 (2002)