Journal of Applied Nonlinear Dynamics
A Numerical Approach for Solving Nonlinear Singularly Perturbed Boundary Value Problem Arising in Control Theory
Journal of Applied Nonlinear Dynamics 10(1) (2021) 151159  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
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Abstract
In this paper, a numerical approach based on noniterative 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 noniterative 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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