Legendre spectral multi-projection methods for Fredholm integral equations of the first kind

Numerical solution of the first kind Fredholm integral equations using a regularized projection method.

“…In recent years, several researchers have made significant advancements in the field of solving integral equations of the first kind. These advancements encompass a range of regularization techniques, such as collocation methods [5][6][7], multilevel methods [8,9], multiscale methods [10][11][12], projection methods [13][14][15][16][17], and other approaches that have been explored in previous works such as [18,19].…”

“…The proposed approach combines Tikhonov regularization and the projection method to achieve rapid convergence of the discrete equation solutions. It is distinct from the projection methods introduced in [13][14][15][16][17], which primarily utilize projection operators to approximate the compact operator A into discrete operator with a range in R n . Additionally, they employ Tikhonov regularization to address the ill-posedness of the discrete equation and obtain a stable approximate solution.…”