The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
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,...
Homogeneous differential equations with constant coefficients are analysed in the paper to show how extremely high accuracy and speed of computations can be obtained using Taylor series for numerical solutions of differential equations. Two examples of homogeneous differential equations and their solutions by the modern Taylor series method will be analysed in this paper. The main idea behind the...
The paper deals with semi-analytical computations and gives the examples of absolutely exact solutions that can be obtained using numerical solutions of differential equations. Numerical solutions of differential equations based on the Taylor series are implemented in a simulation language TKSL. Polynomials functions, finite integrals, Fourier series and exponential functions are but a few examples...
The simulation language TKSL and modern Taylor series method has proved to be very powerful computing tools for extremely exact, stable and fast numerical solutions of systems of differential equations. In a natural way, TKSL also involves solutions of problems that can be reduced to solving a system of differential equations. It is known that the Taylor series method is a parallel one and therefore...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.