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A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems

Mustafa G 1 , Baleanu D 2 , Ejaz ST 3 , Anjum K 1 , Ahmadian A 4 , Salahshour S 5 Show all authors , Ferrara M 6

Affiliations 

  • 1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
  • 2 Department of Mathematics, Cankaya University, Ankara 06530, Turkey
  • 3 Department of Mathematics, The Government Sadiq College Women University, Bahawalpur 63100, Pakistan
  • 4 Institute of IR 4.0, The National University of Malaysia, 43600 UKM, Bangi, Selangor, Malaysia
  • 5 Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
  • 6 Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy
Math Biosci Eng, 2020 09 28;17(6):6659-6677.
PMID: 33378870 DOI: 10.3934/mbe.2020346

Abstract

In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly per-turbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engi-neering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.

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