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    On Solving Linear and Nonlinear Sixth-Order Two Point Boundary Value Problems Via an Elegant Harmonic Numbers Operational Matrix of Derivatives

    W.M. Abd- Elhameed1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 159-185, 2014, DOI:10.3970/cmes.2014.101.159

    Abstract This paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or More >

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