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The application of Taylor series has become a standard concept in numerical analysis. Their ability of approximating functions arbitrarily close under certain conditions makes them an ideal tool for the integration of differential equations. Before the appearance of digital computers the analytical determination of Taylor series coefficients, i.e. the calculation of higher derivatives, was regarded...
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...
It is the aim of the paper to give some of the basic philosophy of analogue computation before entering into a detailed discussion of the theory of analogue principles. The analogue technique has, in general, three control states; they are the reset, operate, and hold states. The idea of analogue principles is used in our Taylor series integrators. Again, three control states are applied (reset, operate,...
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