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In this chapter, non-polynomial spline functions are applied to develop numerical methods for obtaining smooth approximations for the following BVP: 6 , , , / , D y x f x y a x b D d dx (3.1) subject to the boundary conditions: 2 4 0 2 4 2 4 0 2 4 , , , , ,. y a A D y a A D y a A y b B D y b B D y b B (3.2) where y x and (,)… (More)

In this article, using non-polynomial cubic spline we develop the classes of methods for the numerical solution of singularly perturbed two-point boundary-value problems. The purposed methods are second-order and fourth-order accurate and applicable to problems both in singular and non-singular cases.Numerical results are given to illustrate the efficiency… (More)

Quartic non-polynomial splines are used to develop a new numerical method for computing approximations to the solution of a system of third-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is shown that the new method gives approximations, which are better than those produced by other collocation,… (More)

A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and… (More)