Numerical solutions for a class of singular boundary value problems arising in the theory of epitaxial growth

Abstract

Purpose

This paper aims to apply an iterative numerical method to find the numerical solution of the nonlinear non-self-adjoint singular boundary value problems that arises in the theory of epitaxial growth.

Design/methodology/approach

The proposed problem has multiple solutions and it is singular too; so not every technique can capture all the solutions. This study proposes to use variational iterative numerical method and compute both the solutions. The computed solutions are very close to the exact result.

Findings

It turns out that the existence or nonexistence of numerical solutions fully depends on the value of a parameter. The authors show that numerical solutions exist for small positive values of this parameter. For large positive values of the parameter, they find nonexistence of solutions. They also observe existence of solutions for negative values of the parameter and determine the range of parameter values which separates existence and nonexistence of solutions. This parameter has a clear physical meaning, as it describes the rate at which new material is deposited onto the system. This fact allows interpreting the physical significance of the results.

Originality/value

The authors could capture both the solutions and got accurate estimation of the parameter. This method will be a great tool to handle such types of nonlinear non-self-adjoint equations that have multiple solutions in engineering and mathematical sciences. The results in this paper will have an impact on the understanding of theoretical models of epitaxial growth in near future.

Citation

Verma, A.K., Pandit, B. and Escudero, C. (2020), "Numerical solutions for a class of singular boundary value problems arising in the theory of epitaxial growth", Engineering Computations, Vol. 37 No. 7, pp. 2539-2560. https://doi.org/10.1108/EC-08-2019-0360