Approximation de problèmes fonctionnels et problèmes aux valeurs propres par quasi-interpolants splines. Doctorat thesis (2018), Université de Batna 2.

Abstract

Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally,we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature.Moreover, we provide a convergence analysis and we give new error bounds. Lastly, we exhibit some numerical examples and compare them with previous results in the literature.