A new iteration method for the solution of third-order BVP via Green's function

Abstract

In this study, a new iterative method for third-order boundary value problems based on embedding 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 demonstrated 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
• 47h10
• 47j05