NUMERICAL ANALYSIS OF THE CAUCHY PROBLEM FOR A WIDE CLASS FRACTAL OSCILLATORS

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

THE RICCATI EQUATION WITH VARIABLE HEREDITY

We consider the Riccati differential equation with a fractional derivative of variable order. The introduction of a derivative of a fractional variable order into the initial equation determines the property of the mediu...

BUILDING A STRAIGHT LINE PERPENDICULAR TO A GIVEN LINE

The paper deals with the problem of constructing a straight line perpendicular to a given line, and on constructing a line perpendicular to a given plane, as a rule, reduce to constructing the height of some triangle. In...

ON ONE PROBLE FOR HIGHER-ORDER EQUATION

In this paper not well posed problem for the even-order equation is studied. The stability of the problem is restored by additional conditions and conditions to domain.

USE OF COMPUTER MEANS OF TEACHING THE LESSONS OF GEOMETRY WITH A VIEW TO THE DEVELOPMENT OF THE GEOMETRIC SKILLS OF STUDENTS

This article reviews the methods of application of learning software. Conduct research shows that using a computer on a geometry lesson develops skills of students, making the learning process more effective.

ON THE OPTIMIZATION OF THE CONSTRUCTIVE METHOD OF TRAINING NEURAL NETWORKS

The article suggests a constructive method for training neural networks in which neurons added just before the current epoch of training assume the main training load on the new class to ensure the stability of the netwo...

Download PDF file
  • EP ID EP505449
  • DOI 10.18454/2079-6641-2018-21-1-93-116
  • Views 105
  • Downloads 0

How To Cite

Roman Parovik (2018). NUMERICAL ANALYSIS OF THE CAUCHY PROBLEM FOR A WIDE CLASS FRACTAL OSCILLATORS. Вестник КРАУНЦ. Физико-математические науки, 1(), 93-116. https://europub.co.uk/articles/-A-505449