Numerical Simulation and Analysis of Systems with Memory Based on Integro-Differentiation of Fractional Order

2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT) Pub Date : 2018-09-01 DOI:10.1109/STC-CSIT.2018.8526702

Yaroslav Sokolovskyy, M. Levkovych, O. Mokrytska, Yaroslav Kaplunskyy

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引用次数: 1

Abstract

Mathematical models are constructed and numerical methods are devised for investigation of deformation-relaxation and heat-mass exchange processes in the environment of fractal structure, taking into account memory effects and spatial correlation. Mathematical models based on integro-differentiation of fractional order to describe the evolution of physical systems with residual memory and self-similarity of fractal structure are obtained. They occupy an intermediate position between Markov's systems and systems which are characterized by complete memory. In particular, the fractional index indicates the share of system states that are stored throughout the process of its functioning. Algorithmic support for numerical simulation of environments of fractal structure is developed, which includes the development of parallel algorithms for the implementation of mathematical models.

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基于分数阶积分微分的记忆系统数值模拟与分析

考虑记忆效应和空间相关性，建立了分形结构环境下的变形松弛和热质交换过程的数学模型和数值方法。建立了基于分数阶积分微分的数学模型来描述具有残余记忆和分形结构自相似的物理系统的演化。它们处于马尔可夫系统和完全记忆系统之间的中间位置。特别是，分数索引表示在整个系统运行过程中存储的系统状态的份额。开发了分形结构环境数值模拟的算法支持，其中包括开发用于实现数学模型的并行算法。

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2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT)

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