IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v503y2018icp1189-1203.html
   My bibliography  Save this article

An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics

Author

Listed:
  • Hashemizadeh, E.
  • Ebrahimzadeh, A.

Abstract

The numerous applications of time fractional partial differential equations in different fields of science especially in fluid mechanics necessitate the presentation of an efficient numerical method to solve them. In this paper, Galerkin method and operational matrix of fractional Riemann–Liouville integration for shifted Legendre polynomials has been applied to solve these equations. Some definitions for fractional calculus along with some basic properties of shifted Legendre polynomials have also been put forth. When approximations are substituted into the fractional partial differential equations, a set of algebraic equations would be resulted. The convergence of the suggested method was also depicted. In the end, the linear time fractional Klein–Gordon equation, dissipative Klein–Gordon equations and diffusion-wave equations were utilized as three examples so as to study the performance of the numerical scheme.

Suggested Citation

  • Hashemizadeh, E. & Ebrahimzadeh, A., 2018. "An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1189-1203.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:1189-1203
    DOI: 10.1016/j.physa.2018.08.086
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118310288
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.08.086?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daria Kondrashova & Rustem Valiullin & Jörg Kärger & Armin Bunde, 2017. "Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(7), pages 1-6, July.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li Jiang & Tao Wang & Qing-Xue Huang, 2023. "Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations," Mathematics, MDPI, vol. 11(7), pages 1-15, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jonas Mockus, 2010. "On simulation of optimal strategies and Nash equilibrium in the financial market context," Journal of Global Optimization, Springer, vol. 48(1), pages 129-143, September.
    2. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2022. "Globalization, long memory, and real interest rate convergence: a historical perspective," Empirical Economics, Springer, vol. 63(5), pages 2331-2355, November.
    3. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    4. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    5. Youwei Li & Xue-Zhong He, 2005. "Long Memory, Heterogeneity, and Trend Chasing," Computing in Economics and Finance 2005 113, Society for Computational Economics.
    6. Ra l De Jes s Guti rrez & Lidia E. Carvajal Guti rrez & Oswaldo Garcia Salgado, 2023. "Value at Risk and Expected Shortfall Estimation for Mexico s Isthmus Crude Oil Using Long-Memory GARCH-EVT Combined Approaches," International Journal of Energy Economics and Policy, Econjournals, vol. 13(4), pages 467-480, July.
    7. Christos Christodoulou-Volos & Fotios Siokis, 2006. "Long range dependence in stock market returns," Applied Financial Economics, Taylor & Francis Journals, vol. 16(18), pages 1331-1338.
    8. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    9. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    10. Naimoli, Antonio, 2022. "Modelling the persistence of Covid-19 positivity rate in Italy," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    11. Mehmet Dalkir, 2005. "A New Method For Estimating The Order Of Integration Of Fractionally Integrated Processes Using Bispectra," Econometrics 0507001, University Library of Munich, Germany, revised 07 Jul 2005.
    12. Richard T. Baillie & Fabio Calonaci & Dooyeon Cho & Seunghwa Rho, 2019. "Long Memory, Realized Volatility and HAR Models," Working Papers 881, Queen Mary University of London, School of Economics and Finance.
    13. Muniandy, Sithi V. & Uning, Rosemary, 2006. "Characterization of exchange rate regimes based on scaling and correlation properties of volatility for ASEAN-5 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 585-598.
    14. Boubaker Heni & Canarella Giorgio & Miller Stephen M. & Gupta Rangan, 2017. "Time-varying persistence of inflation: evidence from a wavelet-based approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-18, September.
    15. Guglielmo Maria Caporale & Luis A. Gil-Alana & Carlos Poza, 2021. "Cycles and Long-Range Behaviour in the European Stock Markets," Dynamic Modeling and Econometrics in Economics and Finance, in: Gilles Dufrénot & Takashi Matsuki (ed.), Recent Econometric Techniques for Macroeconomic and Financial Data, pages 293-302, Springer.
    16. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    17. Rocha Souza, Leonardo & Jorge Soares, Lacir, 2007. "Electricity rationing and public response," Energy Economics, Elsevier, vol. 29(2), pages 296-311, March.
    18. Roger Newson, 2001. "Update to somersd," Stata Technical Bulletin, StataCorp LP, vol. 10(57).
    19. Hassler, Uwe & Marmol, Francesc, 1998. "Fractional cointegrating regressions in the presence of linear time trends," DES - Working Papers. Statistics and Econometrics. WS 9794, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Yuliya Lovcha & Alejandro Perez-Laborda, 2017. "Structural shocks and dynamic elasticities in a long memory model of the US gasoline retail market," Empirical Economics, Springer, vol. 53(2), pages 405-422, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:1189-1203. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.