IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v396y2021ics0096300320308845.html
   My bibliography  Save this article

Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations

Author

Listed:
  • Liu, Hongyan
  • Huang, Jin
  • Zhang, Wei

Abstract

The barycentric form of Lagrange interpolant is attractive due to its stability, fast convergent rate, high precision and so on. In this paper, we applies an algorithm based on two dimensional extension of barycentric Lagrange interpolant for solving two dimensional integro-differential equations (2D-IDEs) numerically. First, the solution of the 2D-IDEs is replaced by the extended two dimensional barycentric Lagrange interpolant which is constructed by tensor product nodes, the set of differential operators is discretized by the differential matrix of barycentric interpolant, the double integral is approximated by an extended Gauss-type quadrature formula and the boundary conditions are treated by the substitute method. Then the solution of the 2D-IDEs is transformed into the solution of the corresponding system of algebraic equations. The error estimation and convergence analysis are also discussed. Last, several numerical examples are given to demonstrate the merits of the current method.

Suggested Citation

  • Liu, Hongyan & Huang, Jin & Zhang, Wei, 2021. "Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308845
    DOI: 10.1016/j.amc.2020.125931
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320308845
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125931?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. Hongchun Wu & Yulan Wang & Wei Zhang, 2018. "Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-10, December.
    2. Liu, Hongyan & Huang, Jin & Zhang, Wei & Ma, Yanying, 2019. "Meshfree approach for solving multi-dimensional systems of Fredholm integral equations via barycentric Lagrange interpolation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 295-304.
    3. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    4. Rohaninasab, N. & Maleknejad, K. & Ezzati, R., 2018. "Numerical solution of high-order Volterra–Fredholm integro-differential equations by using Legendre collocation method," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 171-188.
    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. Zhiwu Zhou & Julián Alcalá & Víctor Yepes, 2022. "Research on Sustainable Development of the Regional Construction Industry Based on Entropy Theory," Sustainability, MDPI, vol. 14(24), pages 1-23, December.

    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. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    2. Fernández Lexuri & Hieber Peter & Scherer Matthias, 2013. "Double-barrier first-passage times of jump-diffusion processes," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 107-141, July.
    3. Zailei Cheng, 2017. "Optimal dividends in the dual risk model under a stochastic interest rate," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-16, March.
    4. Kyriakos Georgiou & Athanasios N. Yannacopoulos, 2023. "Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9," Papers 2309.12384, arXiv.org.
    5. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    6. Peter K. Friz & Stefan Gerhold & Marc Yor, 2013. "How to make Dupire's local volatility work with jumps," Papers 1302.5548, arXiv.org.
    7. Belomestny, Denis & Reiß, Markus, 2006. "Spectral calibration of exponential Lévy Models [2]," SFB 649 Discussion Papers 2006-035, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Bogdan Căruntu & Mădălina Sofia Paşca, 2021. "The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    9. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    10. Hainaut, Donatien & Leonenko, Nikolai, 2020. "Option pricing in illiquid markets: a fractional jump-diffusion approach," LIDAM Discussion Papers ISBA 2020003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    12. Kathrin Glau, 2015. "Feynman-Kac formula for L\'evy processes with discontinuous killing rate," Papers 1502.07531, arXiv.org, revised Nov 2015.
    13. Nemat Safarov & Colin Atkinson, 2017. "Natural Gas-Fired Power Plants Valuation And Optimization Under Lévy Copulas And Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-38, February.
    14. repec:hum:wpaper:sfb649dp2012-017 is not listed on IDEAS
    15. Andrey Itkin & Dmitry Muravey, 2023. "American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support," Papers 2307.13870, arXiv.org.
    16. Peter Friz & Stefan Gerhold, 2011. "Don't stay local - extrapolation analytics for Dupire's local volatility," Papers 1105.1267, arXiv.org.
    17. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    18. Jakub Drahokoupil, 2020. "Variance Gamma process in the option pricing model," FFA Working Papers 3.002, Prague University of Economics and Business, revised 31 Jan 2021.
    19. Nemat Safarov & Colin Atkinson, 2016. "Natural gas-fired power plants valuation and optimisation under Levy copulas and regime-switching," Papers 1607.01207, arXiv.org, revised Jul 2016.
    20. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta Hedging in a Jump-Diffusion Model," Papers 1910.08946, arXiv.org, revised Apr 2022.
    21. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.

    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:396:y:2021:i:c:s0096300320308845. 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.