A Monotone Iterative Technique for Nonlinear Fourth Order Elliptic Equations with Nonlocal Boundary Conditions

Abstract

This paper proposes an accelerated iterative procedure for a nonlinear fourth order elliptic equation with nonlocal boundary conditions. First, an existence and uniqueness theorem is proved for the fourth order elliptic equation via the accelerated iterative procedure. To solve this problem numerically, a finite difference based numerical scheme is also developed in view of the main theorem. Theoretically, the monotone property as well as the convergence analysis are proved for both the continuous and discretized cases. The main result also supplements several algorithms for computing the solution of the fourth order elliptic integro-partial differential equation. The proposed scheme not only accelerates the scheme in the literature but also provides a greater flexibility in choosing the initial guess. The efficacy of the proposed scheme is demonstrated through a comparative numerical study with the recent literature. The numerical simulation confirms the theoretical claims too.