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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.
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https://hal.archives-ouvertes.fr/hal-00853599
Contributor : Isabelle Charpentier Connect in order to contact the contributor
Submitted on : Friday, September 20, 2013 - 10:06:33 AM
Last modification on : Wednesday, December 1, 2021 - 3:32:11 PM
Long-term archiving on: : Friday, April 7, 2017 - 12:18:54 AM

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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. 2013. ⟨hal-00853599v2⟩

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