We emphasized explicitly on the derivation and implementation of a new\nnumerical algorithm scheme which gave stable results that show the applicability\nof the method. In this paper, we aimed to solve some second order initial\nvalue problems of ordinary differential equations and compare the results\nwith the theoretical solution. Using this method to solve some initial value\nproblems of second order ordinary differential equations, we discovered that\nthe results compared favorably with the theoretical solution which led to the\nconclusion that the new numerical algorithm scheme derived in the research\nis approximately correct and can be prescribed for any related ordinary differential\nequations.
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