A new iteration method for the solution of third-order BVP via Green's function - Akgun, Fatma Aydin; Rasulov, Zaur (DE GRUYTER POLAND SP Z O O, 2021)
In this study, a new iterative method for third-order boundary value problems based on embed-ding Green's function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demon-strated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.
Keywords: boundary value problem; fixed point iteration method; Green's function; integral operator; rate of convergence; MULTIPLE POSITIVE SOLUTIONS; EXISTENCE; Mathematics