COMPARISON OF METHODS OF CONSTRUCTION OF APPROXIMATE ANALYTICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS CONSIDERING ON THE EXAMPLE OF ELEMENTARY FUNCTIONS
Abstract
Compares methods of constructing multilayer approximate solutions of differential equations based on classical approximate methods on the example of the exponent and cosine. In contrast to classical numerical methods, this approach allows to obtain not point wise approximation, and approximate solutions as functions. Considered approach, based on explicit and implicit Euler methods, one-step Adams method, Runge-Kutta second-order method, and Stermer method. A comparison of the accuracy of the formula obtained using the method of Adams for exhibitors and Stermer method for the cosine partial sum of the McLaren series. The comparison carried out with the same number of completed operations of addition/subtraction and multiplication/division and the same degree of decomposition. Computational experiments showed the advantage of the proposed formulas. The proposed methods are tested on the search task period of the solution of a differential equation.
References
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