WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 17, 2018
An Efficient Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems
Authors: ,
Abstract: In this paper, a new numerical integration method on a uniform mesh is presented for the solution of singularly perturbed two-point boundary value problems having boundary layer at one end (left or right) point. The methods of Exact and Trapezoidal rule of integration with finite difference approximation of first derivatives are used to obtain a three-term recurrence relationship . The obtained tridiagonal system of equations is then solved using Thomas algorithm. Also, the stability and convergence of the proposed scheme are established. Several model example problems are solved using the proposed method. The results are presented in terms of maximum absolute errors which demonstrate the accuracy and efficiency of the method. It is observed that the proposed method is capable of producing highly accurate results with minimal computational effort for a fixed value of step size h, when perturbation parameter tends to zero.
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Keywords: Singular perturbation problems, Bounary value problems, Stability and convergence, Numerical Integration
Pages: 265-273
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #33