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Theoretical and numerical analysis for Volterra integro-differential equations with Itô integral under polynomially growth conditions

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  • Yang, Huizi
  • Yang, Zhanwen
  • Ma, Shufang

Abstract

In this paper, we theoretically and numerically deal with nonlinear Volterra integro-differential equations with Itô integral under a one-sided Lipschitz condition and polynomially growth conditions. It is proved that both the exact solutions and vector fields are bounded and satisfy a Hölder condition in the pth moment sense. Analogously, the boundedness and Hölder condition in the pth moment sense are preserved by the semi-implicit Euler method for sufficiently small step-size. Moreover, by the local truncated errors, we prove the strong convergence order 1. Finally, numerical simulations on stochastic control models and stochastic Ginzburg–Landau equation illustrate our results.

Suggested Citation

  • Yang, Huizi & Yang, Zhanwen & Ma, Shufang, 2019. "Theoretical and numerical analysis for Volterra integro-differential equations with Itô integral under polynomially growth conditions," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 70-82.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:70-82
    DOI: 10.1016/j.amc.2019.03.053
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    Cited by:

    1. James Hoult & Yubin Yan, 2024. "Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    2. Yang, Xiaochen & Yang, Zhanwen & Zhang, Chiping, 2023. "Numerical analysis of the Linearly implicit Euler method with truncated Wiener process for the stochastic SIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 1-14.

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