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SUMMARYCubic basis functions in one dimension for the solution of two-point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r, where 1 Qr< co. A Galerkin finite element method using the constructed basis functions for the cases r = 1,2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.

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