### Mathematical Biosciences and Engineering

2020, Issue 6: 6659-6677. doi: 10.3934/mbe.2020346
Research article

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

• Received: 27 June 2020 Accepted: 29 July 2020 Published: 28 September 2020
• 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.

Citation: Ghulam Mustafa, Dumitru Baleanu, Syeda Tehmina Ejaz, Kaweeta Anjum, Ali Ahmadian, Soheil Salahshour, Massimiliano Ferrara. A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6659-6677. doi: 10.3934/mbe.2020346

### Related Papers:

• 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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