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A New Algorithm for the Approximation of Initial Value Problems
Abstract
In this paper we present a variable step scheme for the numerical approximation of the initial value problem for ordinary differential equations of an arbitrary order . The scheme is based on quadratic approximation of the solution function and its derivatives up to order , then a half step is performed to approximate st derivative. The whole solution is then extrapolated for more accuracy and for purposes of local error estimation and step size determination. The work overcomes shortcomings of earlier published work and the numerical examples show that the method is quite robust and accurate. A study of the stability properties of the method is also included.
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