A parameter-uniform method for singularly perturbed turning point problems exhibiting interior or twin boundary layers. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Kumar, Devendra
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 5(2019)
• Page Start: 865
• Page End: 882
• Publication Date: 2019-05-04
• Subjects: Singular perturbation problems -- interior layers -- boundary layers -- turning points -- fitted-mesh -- collocation method; 65L10 -- 65L11 -- 65L20 -- 65L50 -- 65L70; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1458098
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: A numerical scheme for a class of two-point singularly perturbed boundary value problems with an interior turning point having an interior layer or twin boundary layers is proposed. The solution of this type of problem exhibits a transition region between rapid oscillations and the exponential behaviour. The problem with interior turning point represents a one-dimensional version of stationary convection–diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. To solve these problems numerically, we consider a scheme which comprises quintic B-spline collocation method on an appropriate piecewise-uniform mesh, which is dense in the neighbourhood of the interior/boundary layer(s). The method is shown to be parameter-uniform with respect to the singular perturbation parameter ϵ . Some relevant numerical examples are illustrated to verify the theoretical aspects computationally. The results compared with other existing methods show that the proposed method provides more accurate solutions.