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Applied Physics and Mathematics

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NUMERICAL SOLUTION OF DIRECT AND INVERSE PROBLEMS FOR THE PARTIAL DERIVATIVE EQUATIONS USING A BASIS WITH STRONG LINEAR INDEPENDENCE
V.А. LEUS

The process of differential-stipulated generation of a function of many variables on Rm that satisfies certain requirements in a finite number of points is considered. With dimension m≥2, guaranteed finding of such a function is impossible. However, the property of strong linear independence of the basic functions allows one to construct approximating functions with a probability close to unity, which is reflected in the concept of almost reliable solvability. On this 2 basis, a new approach to solving direct and inverse problems for partial differential equations is developed. This approach essentially uses the modeling of the sought solutions by combinations of basic functions. It is shown that the linear algebra technique is applicable for obtaining stochastically guaranteed solutions.
Keywords: generating multivariable function, strong linear independence of the basis, almost certain solvability, solution of direct and inverse problems for partial derivative equations.


DOI: 10.25791/pfim.04.2021.1203

Pp. 10-16.

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