Collocation methods for solving multivariable integral equations of the second kind.

Chafik Allouch (1) , Paul Sablonnière (2) , Driss Sbibih (1)

1 Université Mohammed Premier [Oujda]
2 IRMAR - Institut de Recherche Mathématique de Rennes

In a recent paper (Allouch, in press) [5] on one dimensional integral equations of the second kind, we have introduced new collocation methods. These methods are based on an interpolatory projection at Gauss points onto a space of discontinuous piecewise polynomials of degree r which are inspired by Kulkarni's methods (Kulkarni, 2003) [10], and have been shown to give a 4r+4 convergence for suitable smooth kernels. In this paper, these methods are extended to multi-dimensional second kind equations and are shown to have a convergence of order 2r+4. The size of the systems of equations that must be solved in implementing these methods remains the same as for Kulkarni's methods. A two-grid iteration convergent method for solving the system of equations based on these new methods is also defined.

Mots clés: Collocation; Integral equations; Interpolatory projections

Domaines: Analyse numérique [math.NA]

Chafik Allouch, Paul Sablonnière, Driss Sbibih. Collocation methods for solving multivariable integral equations of the second kind.. Journal of Computational and Applied Mathematics, 2012, 236 (17), pp.4494-4512. ⟨10.1016/j.cam.2012.04.020⟩. ⟨hal-00776602⟩