Numerical solution of second order self-adjoint singularly perturbed boundary value problems via quintic B-spline method with fitted mesh

Ram Kishun Lodhi; Hradyesh Kumar Mishra

Ram Kishun Lodhi Symbiosis International University, Symbiosis Institute of Technology, Pune
Hradyesh Kumar Mishra Department of Applied Science and Humanities\\ Kamla Nehru Institute of Technology\\ Sultanpur-228118 (U.P.), India.

Abstract

In this manuscript, a quintic B-spline method (QBSM) is described to calculate the numerical
solution of second order self-adjoint singularly perturbed boundary value problems (SPBVPs).
The piecewise uniform mesh points are generated by using the fitted mesh technique (FMT). The
QBSM is applied directly to the SPBVPs which provides a pentadiagonal linear system and
coefficient matrix is non-singular. Convergence of the proposed technique is studied and
found that it gives fourth order convergence results. The QBSM is applied on two numerical
examples which exhibit the effectiveness of technique.