Abstract
The present work deals with the resolution of the Ginzburg–Landau envelope equation. It is a nonlinear partial differential equation that requires a robust solver. Nowadays, Newton methods are available in many existing commercial codes. However, the computation of the associated tangent operator and its factorization at each incremental step requires a computational cost. In order to reduce this computational cost, we focus on the use of a high-order solver. This algorithm, named in this work (ANM-SM), is made by associating the Asymptotic Numerical Method (ANM) with the Spectral Method (SM). The efficiency and robustness of the used algorithm are illustrated by numerical results of a simple example of a beam resting on a non-linear Winkler foundation.
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