Method of reduction of order for solving singularly perturbed two-point boundary value problems

A collection of computational techniques for solving singular boundary-value problems

“…This technique may be extended to derive other numerical methods, not necessarily limited to tension spline methods. (20) Reddy and Pramod Chakravarthy [39], present a linear and non-linear singularly perturbed two-point boundary-value problem of the form: À ey 00 ðxÞ À aðxÞy 0 ðxÞ þ bðxÞyðxÞ ¼ f ðxÞ;…”

Numerical Solution of Singularly Perturbed Two-Point Boundary Value Problem via Liouville-Green Transform

“…In recent years, a large number of special methods have been developed to provide accurate numerical solutions. For details one may refer to the books of [1][2][3][4][5] and the references [6][7][8][9][10][11]. Many of these methods consist of: 1) dividing the problem into an inner region (boundary layer) problem and an outer region problem; 2) expressing the inner and outer solutions as asymptotic expansions; 3) equating various terms in the inner and outer expressions to determine the constants in these expressions; and 4) combining the inner and outer solutions in some fashion to obtain a uniformly valid solution.…”

A Numerical Scheme for Nonlinear Singularly Perturbed Two point Boundary Value Problems using Locally Exact Integration

“…Bender and Orszag [3], Kevorkian and Cole [4], O' Malley [5], Nay feh [6], Smith [7], Hu et .al [8]. Nu merical methods based on initial value techniques and boundary value techniques are given in [9,10,11,2]. Non linear single step methods for initial value problems were discussed by Van Niekerk [12].…”