Abstract
This paper purpose is to construct maximally parallel algorithms for solving economy problems that are described by dynamic models. The problems of mathematical modeling of a similar class of problems on parallel cluster-type computing systems are considered. Most conventional algorithms for solving such problems (methods of runs, decomposition of a matrix into two diagonal matrices, doubling, etc.), with several processors, usually work no faster than with a single processor. This is caused by significant computations’ sequence of such algorithms. The developed procedure of numerical and analytical sampling is quite simply generalized to other types of differential equations of mathematical physics. In particular, in stationary problems it is easier to localize features and apply high-order schemes in the smoothness areas.
Highlights
The economists, in most cases, face complex problems
It should be noted that in recent decades, the dynamics research of economic systems have possessed a steady trend towards continuous time [3]
The study of macroeconomic processes is run by mathematical methods and models, first of all, by the theory of dynamic systems, which relies on means of differential equations and Laplace transformations
Summary
The economists, in most cases, face complex problems. It is caused by many factors that affect each other, but are determined by time dependencies [1]. The specified class of problems is investigated by economic and mathematical modeling [2]. It should be noted that in recent decades, the dynamics research of economic systems have possessed a steady trend towards continuous time [3]. Economical class of problems with continuous time allows adapting methods and models, and experience of research of linear and nonlinear dynamic systems, accumulated in engineering sciences.
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