Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

• Autorzy: Parovik R. I.

Identyfikatory

DOI

10.1515/acsc-2016-0023

• Języki publikacji: EN

Abstrakty

EN

The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution

Słowa kluczowe

EN

nonlinear hereditary oscillator; finite difference scheme; Cauchy problem; fractional derivatives; numerical experiment

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2016
• Tom: Vol. 26, no. 3
• Strony: 429--435
• Opis fizyczny: Bibliogr. 10 poz., tab., wykr., wzory

Twórcy

autor

Parovik R. I.

• Physics and Mathematics Department, Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, Russian Federation
• Laboratory of Physical Processes Modeling, IKIR FEB RAS, Kamchatka Region, Paratunka, Russian Federation

Bibliografia

• [1] A. M. Nakhushev: Fractional calculus and its applications. Fizmatlit, Moscow. 2003.
• [2] R. I. Parovik: Finite-difference schemes for fractal oscillator with variable fractional orders. Bulletin of Kamchatka Regional Association “Educational Scientific Center” (KRAUNC), Physical and Mathematical Sciences, 2(11), (2015), 88-95. DOI: 10.18454/2079-6641-2015-11-2-88-95.
• [3] R. I. Parovik: Mathematical modeling of hereditary linear oscillators. Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky. 2015.
• [4] R. I. Parovik: Mathematical modeling of the hereditary oscillator. Computer Research and Modeling, 7(5), (2015), 1001-1021.
• [5] R. I. Parovik: On the numerical solution of fractal oscillator equation with time-dependant fractional variable derivative. Bulletin of Kamchatka Regional Association “Educational Scientific Center” (KRAUNC), Physical and Mathematical Sciences, 1(8), (2014), 60-65. DOI: 10.18454/2079-6641-2014-8-1-60-65.
• [6] I. B. Petrov and A. I. Lobanov: Lectures on computational mathematics. BINOM, Moscow. 2006.
• [7] A. A. Samarskii: The theory of difference schemes. Nauka, Mos-cow. 1977.
• [8] S. G. Samko, A. A. Kilbas and O.I. Marichev: Integrals and derivatives of fractional order and some of their applications. Nauka i Tekhnika, Minsk. 1987.
• [9] V. V. Uchaikin: Method of fractional derivatives. Artishok, Ulya-novsk. 2008.
• [10] V. Volterra: Theory of functionals and of integral and integro-differential equations. Nauka, Moscow. 1982.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę