Projection and Multi-projection type methods for linear Fredholm integro-differential equations

This work aims to derive enhanced convergence results for the numerical solutions of linear Fredholm integro-differential equations. We propose a new technique that yields convergence orders of r+1 and 2r for the projection type solution and its iterated version, respectively, using interpolatory or orthogonal projections onto the space of piecewise polynomials of degree at most r-1. Furthermore, by employing multi-projection methods based on the same approximation space, these convergence orders are enhanced to 3r+1 and 4r. The present study extends and improves upon earlier results in the literature. Several numerical examples are provided to illustrate the theoretical findings and to demonstrate the effectiveness of the proposed approaches.