BOUNDARY LAYER-PRESERVING METHODS FOR A CLASS OF NONLINEAR SINGULAR PERTURBATION BOUNDARY VALUE PROBLEMS

Xin Li; Fazhan Geng

doi:10.11948/20220310

2023 Volume 13 Issue 4

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Xin Li, Fazhan Geng. BOUNDARY LAYER-PRESERVING METHODS FOR A CLASS OF NONLINEAR SINGULAR PERTURBATION BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1972-1982. doi: 10.11948/20220310

Citation:

Xin Li, Fazhan Geng. BOUNDARY LAYER-PRESERVING METHODS FOR A CLASS OF NONLINEAR SINGULAR PERTURBATION BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1972-1982. doi: 10.11948/20220310

BOUNDARY LAYER-PRESERVING METHODS FOR A CLASS OF NONLINEAR SINGULAR PERTURBATION BOUNDARY VALUE PROBLEMS

Xin Li^1,,
Fazhan Geng^1, ,

1.
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Author Bio: Email: xinli@amss.ac.cn (X. Li)
Corresponding author: Email: fzg@cslg.edu.cn (F. Z. Geng)
Fund Project: The authors were supported by National Natural Science Foundation of China(Nos. 12101084, 11271100, 11671200), China Postdoctoral Science Foundation(No. 2019M651765) and Natural Science Foundation for the Youth of Jiangsu Province(No. BK20181030). The authors was also supported by Qing Lan Project of Jiangsu Province

Abstract

Abstract

The aim of this paper is to develop a new uniformly convergent numerical approach for nonlinear singularly perturbed boundary value problems (BVPs). The method combines the advantages of the variation-of-constants formula and the reproducing kernel function approximation. It can preserve the boundary layer structure of the solution to the considered singular perturbation problems. In addition, compared with some existing numerical techniques, the present method has no restriction on the choice of nodes. Three numerical experiments are implemented and the numerical results indicate our new technique is quite promising.
- Reproducing kernel method /
- boundary layers /
- nonlinear singularly perturbed problems
MSC: 35A35, 35B30, 65N45

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