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An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations

Author

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  • Singh, P.K.
  • Saha Ray, S.

Abstract

This article discusses the operational matrix method relying on Lucas polynomial to find the solution of multi-dimensional stochastic Itô-Volterra integral equation. For that purpose, the properties of Lucas polynomial and operational matrices have been investigated. Using Lucas polynomial based functions approximations and operational matrices along with collocation points, the multi-dimensional stochastic Itô-Volterra integral equation is converted into a linear or nonlinear system of algebraic equations. Convergence analysis of the presented method has been discussed. Numerical examples are examined to show their computational efficiency and accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:826-845
    DOI: 10.1016/j.matcom.2022.06.029
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    References listed on IDEAS

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    1. 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).
    2. Ting Ke & Guo Jiang & Mengting Deng, 2021. "Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, February.
    3. Behera, S. & Ray, S. Saha, 2020. "An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    4. Mirzaee, Farshid & Solhi, Erfan & Naserifar, Shiva, 2021. "Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Muhammed Çetin & Mehmet Sezer & Coşkun Güler, 2015. "Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-14, February.
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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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