Diamanlab - An interactive Taylor-based continuation tool in MATLAB

Abstract : With the interactive continuation tool Diamanlab, solution branches of a parametric nonlinear problem are computed as sets of Taylor-based solutions stored in checkpoints. Theoretical aspects and implementation are generic, taking advantage of the efficient higher-order asymptotic numerical method in its Diamant form that interprets the generic nonlinear problem as a sequence of linear ones, of Automatic Differentiation (AD) for Taylor coefficient computations, of object-oriented programming and graphical user interface capabilities of MATLAB. The implementation involves four classes devoted to the interactive management of the continuation, to the manipulation of a generic system of nonlinear equations, to the checkpoint management and to higher-order AD, respectively. In practice, any analytical nonlinear system of equation may be implemented in a natural way as a subclass of the generic system class, then solved in an easy manner using the graphical user interface. A benchmark of classical nonlinear problems is provided to serve as a basis for the implementation user-defined problems. Diamanlab usage and bifurcation detection are discussed on the Brusselator problem whose solution involves three interconnected loops. Additional user-defined graphics are presented for the Bratu problem.
Type de document :
Pré-publication, Document de travail
diamanlab_a. 11 pages. 2013
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https://hal.archives-ouvertes.fr/hal-00853599
Contributeur : Isabelle Charpentier <>
Soumis le : vendredi 20 septembre 2013 - 10:06:33
Dernière modification le : vendredi 16 juin 2017 - 10:40:04
Document(s) archivé(s) le : vendredi 7 avril 2017 - 00:18:54

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diamanlab_halb.pdf
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  • HAL Id : hal-00853599, version 2

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Isabelle Charpentier, Bruno Cochelin, Komlanvi Lampoh. Diamanlab - An interactive Taylor-based continuation tool in MATLAB. diamanlab_a. 11 pages. 2013. <hal-00853599v2>

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