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Numerical analysis of the balanced methods for stochastic Volterra integro-differential equations

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Abstract

This thesis mainly proves the strong convergence and the stability in mean-square sense of the implicit balanced methods for the stochastic Volterra integro-differential equations. The balanced implicit methods are proved to give strong convergence rate of 1/2. Furthermore, the paper shows that the balanced implicit methods are stable in mean-square sense with the fully small stepsize. The theoretical results are verified by numerical experiments.

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Acknowledgements

This study was funded by: 1. National Natural Science Foundation of China (Nos. 11801238, 11561028); 2. Jiangxi Provincial Department of Education Youth Fund Project (No. GJJ170566);

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Authors and Affiliations

  1. School of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, Jiangxi, People’s Republic of China

    Lin Hu, Aining Chan & Xuezhong Bao

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  1. Lin Hu
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  2. Aining Chan
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  3. Xuezhong Bao
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Correspondence to Lin Hu.

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Communicated by Hui Liang.

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Hu, L., Chan, A. & Bao, X. Numerical analysis of the balanced methods for stochastic Volterra integro-differential equations. Comp. Appl. Math. 40, 203 (2021). https://doi.org/10.1007/s40314-021-01593-5

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  • DOI: https://doi.org/10.1007/s40314-021-01593-5

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