On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory

• Main Authors: Amit Kumar Verma, Biswajit Pandit, Ravi P. Agarwal
• Format: Article
• Language: English
• Published: Shahid Chamran University of Ahvaz 2020-10-01
• Series: Journal of Applied and Computational Mechanics
• Subjects: singular boundary value problems; nonlinear boundary value problems; iterative method; convergence analysis; multiple solutions; non-self-adjoint operators; epitaxial growth
• Online Access: http://jacm.scu.ac.ir/article_14788_1599ead9dad6950c0438af2e6d10f035.pdf

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to pick multiple solutions together by any discrete method like finite difference method, finite element method etc. Here, we propose a new technique based on homotopy perturbation method and variational iteration method. We compare numerically the approximate solutions computed by Adomian decomposition method. We study the convergence analysis of both iterative schemes in C^2 ([0,1]). For small values of λ, solutions exist whereas for large values of λ solutions do not exist.