Abstract
Influenced by Xiao et al. (J Integral Equations Appl 30(1):197–218, 2018), collocation methods are developed to study strong convergence orders of numerical solutions for nonlinear stochastic Volterra integral equations under the Lipschitz condition in this paper. Some properties of exact solutions are discussed. These properties include the mean-square boundedness, the Hölder condition, and conditional expectations. In addition, this paper considers the solvability, the mean-square boundedness, and strong convergence orders of numerical solutions. At last, we validate our conclusions by numerical experiments.
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Acknowledgements
The authors would like to thank Yang Zhanwen (School of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China.) and Yin Zhi (Institute of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China) for their valuable advice and comments to improve the quality of this work. We also thank reviewers for their valuable advice and comments to improve the quality of this work.
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Communicated by Hui Liang.
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Xu, X., Xiao, Y. & Zhang, H. Collocation methods for nonlinear stochastic Volterra integral equations. Comp. Appl. Math. 39, 330 (2020). https://doi.org/10.1007/s40314-020-01353-x
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DOI: https://doi.org/10.1007/s40314-020-01353-x