A COMPARATIVE STUDY OF ORTHOGONAL POLYNOMIALS FOR NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Abstract
In this paper, we adopt the general method of interpolation and collocation in Linear Multistep Methods in deriving some numerical schemes for solving second order ordinary differential equations. Different choices of the interpolating function in the form of shifted Legendre, shifted Chebyshev and Lucas polynomials with the same interpolation and collocation points are considered in order to establish uniformity or otherwise of the derived schemes for the various polynomials. Furthermore, probable disparities in the derived schemes for varied choices of interpolation and collocation points are also investigated. Results indicate that all the polynomials yield exactly the same schemes for the same choice of interpolation and collocation points but different schemes for different choices of interpolation and collocation points. However, numerical examples considered showed that all the derived schemes performed exactly in the same manner in terms of accuracy, regardless of the choices of interpolation or collocation points. Nevertheless, the derived schemes perform admirably better when compared with existing methods in literature
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