Title: Fourth order computational method for two parameters singularly perturbed boundary value problem using non-polynomial cubic spline
Authors: K. Phaneendra; G. Mahesh
Addresses: Department of Mathematics, University College of Science, Osmania University, Saifabad, Hyderabad, India ' Department of Mathematics, University College of Science, Osmania University, Saifabad, Hyderabad, India
Abstract: In this paper, we proposed a fourth order finite difference scheme using non-polynomial cubic spline for the solution of two parameters singularly perturbed two-point boundary value problem having dual boundary layer on a uniform mesh. In this method, the first order derivatives in the non-polynomial cubic spline finite difference scheme are replaced by the higher order finite differences to get the discretisation equation for the problem. The discretisation equation is solved by the tridiagonal solver discrete invariant imbedding. The proposed method is analysed for convergence and a fourth order rate of convergence is proved. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.
Keywords: two parameters; singularly perturbed; two point boundary value problem; dual boundary layer; characteristic equation; non-polynomial cubic spline.
International Journal of Computing Science and Mathematics, 2019 Vol.10 No.3, pp.261 - 275
Received: 17 Aug 2016
Accepted: 19 Jul 2017
Published online: 24 Jul 2019 *