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

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:

Integro-differential equations , quasi-interpolants , collocation method , Kantorovich method