The solutions of many physical problems are obtained as expansions in series of orthogonal functions. In this paper, construction of new class of orthogonal polynomials is proposed. This class of polynomials is valid in the interval [-1, 1] with respect to constant fractional weight function, 2
Highlights• The paper focused on the numerical solution of higher order initial value problems.• Power series was used as the basis function for the derivation of the method.• The method solved second, third and fourth order ordinary differential equations concurrently.• This method satisfied the basic properties of a linear multistep method.• This method generated more accurate results than the existing numerical methods.
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