This paper is dedicated to presenting and analyzing a numerical algorithm for the solution of even-order boundary value problems. The proposed solutions are spectral and they depend on introducing a new matrix of derivatives of certain shifted Legendre polynomial basis, along with the application of the collocation method. The nonzero elements of the introduced matrix are expressed in terms of the well-known harmonic numbers. Numerical examples provide favorable comparisons with other existing methods and ascertain the efficiency and applicability of the proposed algorithm.
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