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Numerical solution of multi-dimensional Itô Volterra integral equations by the second kind Chebyshev wavelets and parallel computing process

Author

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  • Ahmadinia, M.
  • Afshariarjmand, H.
  • Salehi, M.

Abstract

This paper presents a numerical method based on the least squares method and the second kind Chebyshev wavelets for solving the multi-dimensional Itô Volterra integral equations. The multi-dimensional Itô Volterra integral equation is converted to a non-square linear system of equations by Clenshaw-Curtis quadrature rules, then the least squares solution is obtained by the QR factorization method. As the multi-dimensional Itô Volterra integral equations are computationally intensive, we have used the parallel computing process to find the numerical solutions with reduced computation time. The convergence rate of the presented method is proven. Numerical results show the reliability and efficiency of the presented method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001571
    DOI: 10.1016/j.amc.2023.127988
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    References listed on IDEAS

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    1. 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).
    2. 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).
    3. 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.
    4. 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).
    5. 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.
    6. 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).
    7. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, December.
    8. Gao, Jianfang & Liang, Hui & Ma, Shufang, 2019. "Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 385-398.
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