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This paper is on the development of a new scheme for the solution of initial value problems in ordinary differential equations. We present some basic concepts and fundamental theories which are very vital to the development of the scheme. The new scheme is of order seven and its derivation is based on the representation of the theoretical solution by perturbed polynomial function of degree four. This scheme is suitable for problems associated with the systems of ordinary differential equations having oscillatory or exponential solution.

Development of a New Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations