NUMERICAL ANALYSIS OF THE CAUCHY PROBLEM FOR A WIDE CLASS FRACTAL OSCILLATORS
Journal Title: Вестник КРАУНЦ. Физико-математические науки - Year 2018, Vol 1, Issue
Abstract
The Cauchy problem for a wide class of fractal oscillators is considered in the paper and its numerical investigation is carried out using the theory of finite-difference schemes. Fractal oscillators characterize oscillatory processes with power memory or, in general, with heredity, and are described by means of integro-differential equations with difference kernels — memory functions. By choosing memory functions as power functions, integrodifferential equations are reduced to equations with derivatives of fractional orders. In this paper, using the approximation of the fractional derivatives of Gerasimov-Kaputo, a non-local explicit finite-difference scheme was developed, its stability and convergence are justified, estimates of the numerical accuracy of computational accuracy are presented. Examples of the work of the proposed explicit-finite scheme are given. It is shown that the order of computational accuracy tends to unity as the number of grid nodes increases and coincides with the order of approximation of the explicit finite difference scheme.
Authors and Affiliations
Roman Parovik
Keywords
Related Articles
- EP ID EP505449
- DOI 10.18454/2079-6641-2018-21-1-93-116
- Views 93
- Downloads 0
BOUNDARY VALUE PROBLEM FOR A GENERALIZED TELEGRAPH EQUATION OF FRACTIONAL ORDER WITH VARIABLE COEFFICIENTS
In this paper, we construct the solution to the Goursat problem for a generalized telegraph equation of fractional order with variable coefficients.
VISUAL APPLICATION DESIGN ENVIRONMENT OF OPERATING MODELS FOR ACOUSTIC AND ELECTROMAGNETIC EMISSION SIGNAL PROCESSING AND ANALYSIS
We present a technology of creation of visual application design environment for hardwaresoftware complexes (VDE HSC) aimed at acoustic and electromagnetic emission signal processing and analysis. The technology includes...
OVERHAUSER VECTOR MAGNETOMETER POS-4: THE RESULTS OF CONTINUOUS MEASUREMENTS DURING 2015-2016 AT GEOPHYSICAL OBSERVATORY «PARATUNKA»OF IKIR FEB RAS, KAMCHATKA, RUSSIA
The summary results of the analysis of the measurements by Overhauser vector magnetometer POS-4 during about 1.5 years are presented.
METHODS OF ISOLATION OF ELECTROMAGNETIC LITOSPHRIC SIGNALS
The physical terms of origin and distribution of electromagnetic radiation of litospheric origin and features of registration based on them are examined. Measuring methods offer seismoelectromagnetic activity is paramete...
CRITERIA FOR THE STRESS-STRAIN STATE OF THE MEDIUM AND THE POWER LAW OF RELAXATION
A model of high stress zone in the medium with point sources in the form of double forces is presented. Linear and nonlinear dilatancy criteria is calculated on data from the seismic Havard CMT catalog. Using the example...