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Numerical solution of stochastic Itô-Volterra integral equation by using Shifted Jacobi operational matrix method

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  • Saha Ray, S.
  • Singh, P.

Abstract

In this paper, a numerical method is implemented to solve the stochastic Itô-Volterra integral equations. In this approach, operational matrices have been applied to reduce the stochastic Itô-Volterra integral equations to linear algebraic equations. Then collocation method is applied to solve the algebraic equations. The error, convergence, and stability analysis of the proposed method are discussed. Also, the steps of the proposed method have been presented in the form of an algorithm. Numerical examples are introduced to confirm the efficiency and reliability of the proposed scheme.

Suggested Citation

  • Saha Ray, S. & Singh, P., 2021. "Numerical solution of stochastic Itô-Volterra integral equation by using Shifted Jacobi operational matrix method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005294
    DOI: 10.1016/j.amc.2021.126440
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    References listed on IDEAS

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    1. Zeghdane, Rebiha, 2019. "Numerical solution of stochastic integral equations by using Bernoulli operational matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 238-254.
    2. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    3. K. Maleknejad & M. Khodabin & F. Hosseini Shekarabi, 2014. "Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, March.
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    Cited by:

    1. Singh, P.K. & Saha Ray, S., 2023. "An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 826-845.
    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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