SMOOTH SPLINE SOLUTIONS FOR TWO-POINT BOUNDARY-VALUE PROBLEMS
Abstract
We use uniform quadratic and cubicspline polynomials to derive some consistency relations. Theserelations are then used to develop numerical methods for computingsmooth approximations to the solution and its derivative for asecond order boundary value problem. We study the convergenceanalysis of the methods and we show that the cubic spline methodcan produces better results than the quadratic spline, which donot support the conjecture of Khalifa and Eilbeck [14]. Numericalillustrations are provided to demonstrate the practical use ofour methods.
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