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Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method

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  • Mirzaee, Farshid
  • Solhi, Erfan
  • Naserifar, Shiva

Abstract

In this paper, an attractive idea using moving least squares (MLS) and spectral collocation method is extended to estimate the solution of nonlinear stochastic Volterra integro-differential equations (NSVIDEs) that arise in mathematical modeling of natural systems in financial mathematics, physics, and engineering. An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Another advantage that may be appealing to the readers of this article is that acceptable results can be obtained using a small number of points and basis functions, so the calculations are reduced. Applying the proposed scheme leads to the conversion of the problem into a system of algebraic equations. An error bound is presented to ensure the convergence and reliability of the method. Some illustrative examples are presented to reveal the efficiency and applicability of this technique.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005361
    DOI: 10.1016/j.amc.2021.126447
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    References listed on IDEAS

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    1. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
    2. Peng Hu & Chengming Huang, 2014. "The Stochastic -Method for Nonlinear Stochastic Volterra Integro-Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, October.
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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).
    3. Zare, Farideh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2024. "Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 477(C).

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