ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Numerical Approach for Solving Nonlinear Singularly Perturbed Boundary Value Problem Arising in Control Theory

Journal of Applied Nonlinear Dynamics 10(1) (2021) 151--159 | DOI:10.5890/JAND.2021.03.009

P. Murali Mohan Kumar$^1$, A. S. V. Ravi Kanth$^2$

$^1$ Department of Basic Science and Humanities, GMR Institute of Technology, Rajam, Srikakulam, Andhra Pradesh - 532 127, India

$^2$ Department of Mathematics, National Institute of Technology Kurukshetra, Haryana - 136 119, India

Abstract

In this paper, a numerical approach based on non-iterative integration method with a small deviating argument for nonlinear singularly perturbed two point boundary value problems is discussed. The technique of quasilinearization is used to linearize nonlinear singular perturbation problem into a set of linear singularly perturbed equations. The continuous problem is replaced by an approximate first order differential equation with a delay argument which is non-iterative and then the application of numerical integration method to achieve a recurrence relationship of three terms. To demonstrate the effectiveness the proposed method are experimented with nonlinear problems.

Acknowledgments

The authors would like to express their sincere thanks and gratitude to the editors and reviewers for their insightful comments and suggestions for the improvement of this paper.

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