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This work discusses the Euler’s and Milne’s linear multistep methods for solving initial value problems of the ordinary differential equations. By this for the Euler’s we seek an approximation and for the integral equation with a truncation error . Thereby providing an enhancement accuracy and for the Milne’s method for the integral equation the iterative formula: Converges faster where the local truncation error is sufficiently negligible compared to that of Euler. Hence, the milne’ method is a more accurate approximation method than the Euler’s method. Section three points to the fact that linear multi step method so far discussed is convergent provided it is consistent and stable. This result is achievable if the root conditions are satisfied.
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