IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v296y2017icp1-17.html
   My bibliography  Save this article

An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation

Author

Listed:
  • Behroozifar, M.
  • Sazmand, A.

Abstract

In this article, we present a numerical method to numerically solve a time-fractional convection–diffusion equation. Our method is based on the operational matrices of shifted Jacobi polynomials. At first, problem is converted to a homogeneous problem by interpolation and afterward an integro-differential equation is yielded. Then we approximate the known and unknown functions with the help of shifted Jacobi functions. A system of nonlinear algebraic equations is obtained. Finally, the unknown coefficients are determined by MathematicaTM. We implemented the proposed method for several examples that they indicate the high accuracy method. It should be noted that this method is generalizable to some appropriate problems.

Suggested Citation

  • Behroozifar, M. & Sazmand, A., 2017. "An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 1-17.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:1-17
    DOI: 10.1016/j.amc.2016.09.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316305987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.09.028?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. Abbasbandy, Saeid & Kazem, Saeed & Alhuthali, Mohammed S. & Alsulami, Hamed H., 2015. "Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 31-40.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    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. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    2. Kumar, Devendra & Nama, Hunney & Baleanu, Dumitru, 2024. "Dynamical and computational analysis of fractional order mathematical model for oscillatory chemical reaction in closed vessels," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Singh, Harendra & Srivastava, H.M., 2019. "Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1130-1149.
    4. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    5. Wu, Longyuan & Zhai, Shuying, 2020. "A new high order ADI numerical difference formula for time-fractional convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 387(C).

    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. 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.
    9. Naimoli, Antonio, 2022. "Modelling the persistence of Covid-19 positivity rate in Italy," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    10. 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.
    11. 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.
    12. 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.
    13. Boubaker Heni & Canarella Giorgio & Gupta Rangan & Miller Stephen M., 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.
    14. 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.
    15. 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.
    16. Rocha Souza, Leonardo & Jorge Soares, Lacir, 2007. "Electricity rationing and public response," Energy Economics, Elsevier, vol. 29(2), pages 296-311, March.
    17. Roger Newson, 2001. "Update to somersd," Stata Technical Bulletin, StataCorp LP, vol. 10(57).
    18. 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.
    19. 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.
    20. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona School of Economics.

    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:apmaco:v:296:y:2017:i:c:p:1-17. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.