OPTIMAL METHODS OF THERMAL FIELD APPROXIMATION

Boykov Il'ya Vladimirovich, Doctor of physical and mathematical sciences, professor, head of sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), boikov@pnzgu.ru
Krivulin Nikolay Petrovich, Candidate of engineering sciences, associate professor, sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), krivulin@bk.ru
Ryazantsev Vladimir Andreevich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), ryazantsevv@mail.ru

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Background. The research of thermal fields represents significant importance in solution of multiple physical and technical problems. Suffice it to mention such fields as thermodynamics and thermal prospecting. Thermal fields have a complex structure impossible to be presented analytically. Therefore the methods of uniform approximation appear to be topical in the whole area of determination thereof. Besides the development of methods of uniform approximation of thermal fields it is topical to develop methods of approximation and restoration of thermal fields accu-rate in precision, complexity and memory. In the research of physical fields of various nature there appear the following problems: 1) building of algorithms of uniform approximation of fields in the area under consideration; 2) development of optimal methods of filed approximation in the area under consideration.
Methods and materials. To solve the said problems the authors suggest a method common for physical fields of any nature. To build the best uniform approximation of aphysical field it is necessary to determine the functional class, to which the said field belongs, to calcu-late Kolmogorov and Babenko widths of the corresponding class and to build splines being the optimal method of approximation. The researchers determine the class of funtions, to which belong the solutions of parabolic equations, and build approximations, uniform in C space metrics, of the said solutions in the form of local splines. It is shown that the built algorithm of approximation differs from the optimal one by the multiplication factor.
Results. The study suggests the effective methods of unform restoration of thermal fields.
Conclusions. The results of the study may be used in development of numerical methods of thermal prospecting and thermodynamics problems modeling.

thermal field, uniform approximation, local spline, optimal methods, function class, Kolmogorov width, Babenko width.

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