Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:319

Article

Lodhi, Ram Kishun¹  Mishra, Hradyesh Kumar¹ 

[1] Jaypee Univ Engn & Technol, Dept Math, AB Rd Raghogarh, Guna 473226, MP, India

关键词: Singularly perturbed boundary value problems;    Quintic B-spline method;    Shishkin mesh;    Boundary layers;    Quasilinearization;    Uniform convergence;   

DOI  :  10.1016/j.cam.2017.01.011

来源: Elsevier

【 摘 要 】

In this paper, we have studied a numerical scheme to solve second order singularly perturbed two-point linear and nonlinear boundary value problems. The boundary layer of this type of problems exhibits at one end (left or right) point of the domain due to the presence of perturbation parameter epsilon. The quintic B-spline method and suitable piecewise uniform Shishkin mesh have been used. Linear and nonlinear second order singularly perturbed boundary value problems have been solved by the present method. The convergence analysis is also provided and the method is shown to have uniform convergence of fourth order. Numerical results have demonstrated the efficiency of the present method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free