Geodesic
High-order modified tau method for non-smooth solutions of Abel integral equations
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 462-471.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, the spectral Tau method and generalized Jacobi functions are fruitfully combined to approximate Abel integral equations with solutions that may have singularities (non-smooth solutions) at the origin. In an earlier work of P. Mokhtary and F. Ghoreishi [Electron. Trans. Numer. Anal., 41 (2014), pp. 289 -- 305], a regularization process was used to handle the high-order Tau method based on classical Jacobi polynomials for the numerical solution of Abel integral equations. However, it was found that this scheme makes the resulting equation and its Tau approximation more complicated. In this work, we introduce and analyze a new modified Tau method for the numerical solution of Abel integral equations with non-smooth solutions. The main advantage of this method is that it gains a high order of accuracy without adopting any regularization process. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.
Classification : 45E10, 41A25
Keywords: modified tau method, generalized Jacobi functions, Abel integral equations 
@article{ETNA_2015__44__a8,
     author = {Mokhtary, Payam},
     title = {High-order modified tau method for non-smooth solutions of {Abel} integral equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {462--471},
     publisher = {mathdoc},
     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a8/}
}
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Mokhtary, Payam. High-order modified tau method for non-smooth solutions of Abel integral equations. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 462-471. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a8/