Collocation methods for solving multivariable integral equations of the second kind

• Autores: C. Allouch, Paul Sablonnière , D. Sbibih
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 17, 2012, págs. 4494-4512
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.04.020
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• Resumen

  • 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.