IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v170y2023ics096007792300259x.html
   My bibliography  Save this article

Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model

Author

Listed:
  • Kumar, Yashveer
  • Yadav, Poonam
  • Singh, Vineet Kumar

Abstract

In this manuscript, our goal is to design distributed order Gauss-Quadrature scheme for solving distributed order fractional sub-diffusion mathematical model based on an orthogonal generating polynomial (OGP) with respect to the weight function of distributed order anomalous time-fractional subdiffusion partial differential equation (DOT-FSPDE). Based on OGP we established a new computational algorithm for the DOT-FSPDE, which is controlled by the single input distribution weight function of DOT-FSPDE. The proposed problem has been solved numerically with the help of the OGP-Gauss quadrature rule along with an operational matrix based on the designed OGP technique. Also, we established error bounds, convergence analysis, numerical algorithms, error estimation, numerical stability and theoretical stability analysis of the designed scheme. There are several test examples which have been solved for the reliability of the proposed computational method with less CPU time. The proposed technique was found to be more accurate in comparison with the existing scheme.

Suggested Citation

  • Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s096007792300259x
    DOI: 10.1016/j.chaos.2023.113358
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792300259X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113358?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. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2022. "A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 210-235.
    2. Alikhanov, Anatoly A., 2015. "Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 12-22.
    3. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    4. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    5. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    6. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2019. "A novel Legendre operational matrix for distributed order fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 215-231.
    7. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar & Tohidi, Emran, 2017. "Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 310-321.
    8. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 267-284, September.
    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. Marasi, H.R. & Derakhshan, M.H. & Ghuraibawi, Amer A. & Kumar, Pushpendra, 2024. "A novel method based on fractional order Gegenbauer wavelet operational matrix for the solutions of the multi-term time-fractional telegraph equation of distributed order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 405-424.
    2. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(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. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    2. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Fernandez, Pablo & Ariño, Miguel A., 1996. "Divisas. Evolución y análisis de tipos de cambio (1980-1995)," IESE Research Papers D/315, IESE Business School.
    4. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    5. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    6. Ibrahim Chowdhury & Lucio Sarno, 2004. "Time‐Varying Volatility in the Foreign Exchange Market: New Evidence on its Persistence and on Currency Spillovers," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 759-793, June.
    7. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    10. Al–Zhour, Zeyad & Barfeie, Mahdiar & Soleymani, Fazlollah & Tohidi, Emran, 2019. "A computational method to price with transaction costs under the nonlinear Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 291-301.
    11. Manabu Asai & Michael McAleer, 2011. "Alternative Asymmetric Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 548-564, October.
    12. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    13. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    14. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    15. Roman Horsky & Tilman Sayer, 2015. "Joining The Heston And A Three-Factor Short Rate Model: A Closed-Form Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-17, December.
    16. Jie-Cao He & Hsing-Hua Chang & Ting-Fu Chen & Shih-Kuei Lin, 2023. "Upside and downside correlated jump risk premia of currency options and expected returns," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-58, December.
    17. Frans De Roon & Chris Veld, 1996. "An empirical investigation of the factors that determine the pricing of Dutch index warrants," European Financial Management, European Financial Management Association, vol. 2(1), pages 97-112, March.
    18. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    19. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    20. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.

    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:chsofr:v:170:y:2023:i:c:s096007792300259x. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.