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Optimal selection of orthogonal polynomials applied to the integration of chemical reactor equations by collocation methods |
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| Authors: | L. Lef vre, D. Dochain, S. Feyo de Azevedo,A. Magnus |
| Affiliation: | a GSys Unit, ESISAR, 50 Rue Barthelemy de Laffemas, BP 54, 26902 Valence Cedex 09, France b Cesame, Université Catholique de Louvain, Bât. Euler, av. G. Lemaître 4-6, 1348 Louvain-La-Neuve, Belgium c Departmento de Engeneharia Quimica, Faculdade de Engenheria, Rua dos Bragas, 4099 Porto Codex, Portugal d Numerical Analysis and Applied Mathematics Unit, Université Catholique de Louvain, Bât. de Hemptinne, chemin du Cyclotron 2, 1348 Louvain-La-Neuve, Belgium |
| Abstract: | In this paper, we analyse some properties of the orthogonal collocation in the context of its use for reducing PDE (partial differential equations) chemical reactor models for numerical simulation and/or control design. The approximation of the first order derivatives is first considered and analysed with respect to the transfer of the stability properties of the transport component from the PDE model to its approximated ODE (ordinary differential equations) model. Then the choice of the collocation points as zero of Jacobi polynomial is analysed and interpreted as an optimal choice with respect to a weighted norm. Finally, some guidelines for the use of orthogonal collocation are proposed and the results are illustrated on a simulation example. |
| Keywords: | Partial differential equations Polynomial Orthogonal collocation |
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