Cubic spline method for solving two-point boundary-value problems

In this paper, we use uniform cubic spline polynomials to derive some new consistency relations. These relations are then used to develop a numerical method for computing smooth approximations to the solution and its first, second as well as third derivatives for a second order boundary value problem. The present method outperforms other collocations, finite-difference and splines methods of the same order. Numerical illustrations are provided to demonstrate the practical use of our method.

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