In this paper we derive Non-standard finite difference schemes for the solution of some IVPs emanating from non-autonomous Ordinary Differential Equation. A new technique based on the method of Non-local approximation and renormalization of the denominator function was employed. Numerical experiments were used to verify the reliability of the new Finite Difference schemes proposed for the IVPs and the results obtained shows that the schemes are computationally reliable.

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In this paper, we used an interpolation function with strong trigonometric components to derive a numerical integrator that can be used for solving first order initial value problems in ordinary differential equation. This numerical integrator has been tested for desirable qualities like stability, convergence and consistency. The discrete models have been used for a numerical experiment which makes us conclude that the schemes are suitable for the solution of first order ordinary differential equation.

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A set of new discrete models have been created using Nonstandard methods. A new renormalized denominator function has been derived. This has been applied to some special initial value problems in ordinary differential equation. Result from a suitable numerical solver created from these schemes showed that , the schemes are suitable and they carry along the dynamics of the original equation.