Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation

Authors:
J. KaráTson;B. KováCs
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 3
Cited 0

Iterative solution methods

Iterative solution methods
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Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space

SIAM Journal on Numerical Analysis

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Abstract

An iterative method is developed for nonlinear equations in complex Hilbert spaces, extending the method of variable preconditioning defined earlier in real spaces. We derive convergence of our method. The motivating example for this extension is the time-dependent nonlinear Schrodinger equation, where we use our iteration for the time discretization of the problem and test it numerically.