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A combination method for numerical solution of the nonlinear stochastic Itô-Volterra integral equation

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  • Wen, Xiaoxia
  • Huang, Jin

Abstract

In this article, an efficient combination approach grounded on barycentric rational interpolation and Picard iteration is proposed for solving nonlinear stochastic Itô-Volterra integral equations(SIVIEs). The presented method transforms the SIVIEs into the corresponding algebraic equations whose solution is the expansion coefficients of the barycentric rational interpolation, which is obtained by the Itô-approximation, Gauss-Legendre quadrature formula and Picard iteration algorithm. Moreover, theoretical study confirms that the error and convergence analysis of the approach. In the end, several related numerical experiments are given, which demonstrate the applicability and efficiency of the proposed technique compared with other known numerical methods.

Suggested Citation

  • Wen, Xiaoxia & Huang, Jin, 2021. "A combination method for numerical solution of the nonlinear stochastic Itô-Volterra integral equation," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s009630032100391x
    DOI: 10.1016/j.amc.2021.126302
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    References listed on IDEAS

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    1. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    2. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. Mirzaee, Farshid & Samadyar, Nasrin, 2019. "Numerical solution based on two-dimensional orthonormal Bernstein polynomials for solving some classes of two-dimensional nonlinear integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 344, pages 191-203.
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    Cited by:

    1. P. K. Singh & S. Saha Ray, 2024. "A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-23, June.
    2. Ahmadinia, M. & Afshariarjmand, H. & Salehi, M., 2023. "Numerical solution of multi-dimensional Itô Volterra integral equations by the second kind Chebyshev wavelets and parallel computing process," Applied Mathematics and Computation, Elsevier, vol. 450(C).

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