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In this paper an outline is given of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. Then an extremely accurate and fast method for the numerical solution of ordinary differential equations is presented. In general Taylor series method is not included or even mentioned in surveys on numerical integration...
In this paper an outline is presented of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. The idea of an extremely accurate and fast method for numerical solutions of differential equations is presented in the paper. In general Taylor series are not included or not even mentioned in surveys on numerical...
Methods of numerical solutions of differential equations have been studied since the end of the last century. A large number of integration formulas have been published especially for solving special systems of differential equations. In general, it was not possible to choose the best method but for a subclass of tasks defined by similar properties the most suitable method could always be found. The...
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