Numerical methods based on spline quasi-interpolation operators for integro-differential equations

Document Type : Research Article

Authors

1 University Mohammed I. FPN. MSC Team, LAMAO Laboratory, Nador, Morocco

2 Department of Applied Mathematics, University of Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain

3 Team ANAA, ANO Laboratory , Faculty of Sciences, University Mohammed First, Oujda, Morocco

4 ANO Laboratory , Faculty of Sciences, University Mohammed First, Oujda, Morocco

Abstract

In this paper, we propose collocation and Kantorovich methods based on spline quasi-interpolants defined on a bounded interval  to solve numerically a class of Fredholm integro-differential equations. We describe the computational aspects for calculating the approximate solutions and  give theoretical results corresponding to the convergence order of each method in terms of the degree of the considered spline quasi-interpolant. Finally, we provide some numerical tests that confirm the theoretical results and prove the efficiency of the proposed methods.

Keywords

Journal of Mathematical Modeling
Volume 10, Issue 4
December 2022
Pages 387-401

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