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EnglishWe consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.
| Titolo: | The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Abstract: | We consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments. |
| Handle: | http://hdl.handle.net/11368/2855423 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/130935550 |
| URL: | http://epubs.siam.org/loi/sjnaam |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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