Use of finite difference method for numerical solution of three-dimensional heat transfer fractional differential equation

Authors

  • Gordeeva NO Belgorod State National Research University, Starooskolsky Branch 18 Solnechny microdistrict, 4 Stary Oskol, 309502, Russia
  • Manaeva EN Belgorod State National Research University, Starooskolsky Branch 18 Solnechny microdistrict, 4 Stary Oskol, 309502, Russia
  • Primak IM Belgorod State National Research University, Starooskolsky Branch 18 Solnechny microdistrict, 4 Stary Oskol, 309502, Russia
  • Palasheva II Belgorod State National Research University, Starooskolsky Branch 18 Solnechny microdistrict, 4 Stary Oskol, 309502, Russia

Keywords:

fractional differential equations, heat and mass transfer equation, numerical methods, approximation with fractional derivatives

Abstract

The paper proposes a numerical solution for the mixed problem concerning a three-dimensional heat transfer fractional differential equation, based on the finite difference method. To solve this problem, an explicit difference scheme described in the paper is used. The stability of a proposed difference scheme is proved. The case of homogeneous medium and a square grid is considered.

References

Golovizin V.M., Kisilev V.P., Korotkin I.A. Numerical methods for solving the fractional diffusion equation in the one-dimensional case: Preprint No. IBRAE-2002-10. Moscow: IBRAE RAS, 2002.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo. 2006. Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies). Elsevier Science Inc., New York, NY, USA. ISBN:0444518320.

Bajlekova E. Fractional Evolution Equations in Banach Spaces. Ph. D. Thesis. Eindhoven University of Technology. 2001. – 117 p. url:

https://pure.tue.nl/ws/files/2442305/200113270.pdf (Accessed on 30.12.2018)

Glushak A.V., Primak I.M. Boundary value problems for abstract differential equations with fractional derivatives / Scientific Bulletin of the BelSU. Series: Mathematics. Physics. ISSN: 2075-4639, 2011. - №17 (112). - Issue 24. - Pp.125-140.

Primak I.M. Boundary value problems for abstract fractional differential equations with a bounded operator./Scientific Bulletin of the BelSU. Series: Mathematics. Physics. ISSN: 2075-4639, 2013. - №5 (148). - Issue 30. - Pp.98-106.

Nakhushev A.M. Fractional calculus and its application. Moscow: Fizmatlit, 2003. 272 p.

Beibalaev V.D., Shabanova M.R. A numerical method for solving a boundary value problem for a two-dimensional heat transfer equation with fractional derivatives. Herald of the Samara State Technical University. Series: Physics and mathematics. - 2010. - № 5 (21). - pp. 244–251.

Accessed from: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=vsgtu&paperid=776&option_lang=eng (Accessed on

01.2019)

Taukenova F. I., Shkhanukov-Lafishev M.Kh. Difference methods for solving boundary value problems for fractionalorder differential equations // Comput. Math. Math. Phys., 2006. — Vol. 46, No. 10. — P. 1785–1795. url: https://link.springer.com/article/10.1134/096554250610014 9#citeas (accessed on 22.02.2019)

Lynch V.E., Carreras B.A., del-Castill-Negrete D., FerreiraMejias K.M., Hicks H.R. Numerical methods for the solution of partial differential equations of fractional order // J. Comput. Phys., 2003. — Vol. 192, No. 2. — Pp. 406–421

Babenko Yu.I. The fractional differentiation method in applied problems of heat and mass transfer theory. - SPb: NPO Professional, 2009, 584 p.

S. B. Yuste, and L. Acedo. ―An Explicit Finite Difference Method and a New Von Neumann-Type Stability Analysis for Fractional Diffusion Equations.‖ SIAM Journal on Numerical Analysis, vol. 42, no. 5, 2005, pp. 1862–1874. JSTOR, www.jstor.org/stable/4101366

Samko S.G., Kilbas A.A., Marichev O.I. Fractional integrals and derivatives and some of their applications. Minsk: Science and technology, 1987, 688 p.

Samko S.G., Kilbas, A.A. and O.I. Marichev: Fractional Integrals and Derivatives,: Theory and Applications, Gordon and Breach, Amsterdam 1993. [Engl. Transi, from Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk 1987]‖

Daletsky Yu.L., Krein M.G. Stability of solutions of differential equations in a Banach space. Nauka, Moscow, 1970. - 536 p.

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Published

2024-02-26

How to Cite

Gordeeva, N. O., Manaeva, E. N., Primak, I. M., & Palasheva, I. I. (2024). Use of finite difference method for numerical solution of three-dimensional heat transfer fractional differential equation. COMPUSOFT: An International Journal of Advanced Computer Technology, 8(06), 3197–3200. Retrieved from https://ijact.in/index.php/j/article/view/503

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Section

Original Research Article

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