An iterative technique for a class of highly nonlinear BVP arising in a one-dimensional corneal shape model

Abstract

Purpose

The aim of this work is to establish a computationally efficient iterative technique for solving the highly nonlinear derivative-dependent boundary value problem (DDBVP). The proposed iterative technique is tested on a one-dimensional mathematical model of the shape of the human cornea, which leads to the highly nonlinear DDBVP.

Design/methodology/approach

The approach is a combined venture of quasilinearization along with Picard’s iterative technique. The nonlinear DDBVP is simplified to a sequence of linear problems through a quasilinearization technique. Making use of Picard’s iteration approach, an analogous integral form for the quasilinearized DDBVPs is developed in terms of Green’s function and the convergence controller parameter. The study also covered the convergence analysis of the iterative technique.

Findings

Numerical illustrations are presented to evaluate the applicability, efficiency and accuracy of the technique. The proposed technique provides approximate numerical solutions to the corneal shape model with a variety of constant parameters that can arise in different physical situations. In comparison with existing works, the proposed coupled iterative approach has been found to be more accurate and less computationally complex.

Originality/value

This study introduces an efficient coupled iterative technique based on quasilinearization and Picard’s iterative technique to solve a one-dimensional model of a human cornea. The proposed approach is tested on various physical situations that affect the human cornea. Numerical findings are compared with other published results to demonstrate the method’s efficiency and ease of usage.

Citation

Jyoti and Singh, M. (2024), "An iterative technique for a class of highly nonlinear BVP arising in a one-dimensional corneal shape model", Engineering Computations, Vol. 41 No. 10, pp. 2313-2334. https://doi.org/10.1108/EC-03-2024-0235