About some numerical approaches for mixed integral equations

摘要

In this paper we tackle on mixed Volterra–Fredholm integral equations, as in linear as in non linear cases. To the aim to obtain numerical solutions of these models, the authors propose in the linear case the direct collocation method using a p-order quasi interpolating spline class and in the nonlinear case the fixed point method based on polynomial approximation built by Schauder tensor bases. The advantages of both methods are outlined and their convergence is studied. Numerical results confirm the theoretical statements.