Numerical Solution of the Fredholm Integral Equations of the First Kind by Using Multi-projection Methods

Abstract

The Fredholm integral equations (fies) of the first kind have been solved by Legendre spectral multi-projection methods by using Tikhonov regularized methods. The theoretical analysis utilizing this method under a priori parameter selection strategy has been explained and the best convergence rates obtained in $$L^2$$ -norm. Next, in order to discover an appropriate regularization parameter, Arcangeli’s discrepancy principle has been applied and the order of convergence has been deduced. Numerical example has been furnished which validates our theoretical findings.