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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
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    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.

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