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

Huizi Yang, Zhanwen Yang and Shufang Ma

Applied Mathematics and Computation, 2019, vol. 360, issue C, 70-82

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.

Keywords: Volterra integro-differential equations with Itô integral; Semi-implicit Euler method; Boundedness; Hölder condition; Strong convergence order (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:360:y:2019:i:c:p:70-82

DOI: 10.1016/j.amc.2019.03.053

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