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A new Approach for Solving Linear Ordinary Differential Equations
Abstract
Recently a new numerical scheme, based on series solution method, has been introduced for solving Volterra integral equations. In this work, we make use of the natural relation between ordinary differential equations and Volterra integral equations and apply this approach to initial value problems of linear ordinary differential equations. This study led to approximate solutions, which can be used as algorithms to compute numerical solutions for the initial value problem. This study also introduced special case related to the order of the linear ordinary differential equation and the kernel of the
converted Volterra integral equation. At the end, we investigate the significant features of this approach, by solving selected numerical examples and comparing our results with the results obtained by other methods. Under certain conditions, as in the case if integral equations, we found, that this approach leads to the Taylor expansion of the exact solution.
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