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International Journal of Computer Mathematics Volume 83, 2006 - Issue 10
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Original Articles

Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations

Xiaohua Ding Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, ChinaCorrespondence[email protected]
,
Kaining Wu Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China
&
Mingzhu Liu Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China
Pages 753-761 | Received 01 Jul 2005, Accepted 08 Oct 2006, Published online: 15 Jan 2007

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Haiyan Yuan. (2021) Convergence and stability of exponential integrators for semi-linear stochastic variable delay integro-differential equations. International Journal of Computer Mathematics 98:5, pages 903-932.
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Peng Hu & Chengming Huang. (2011) Stability of stochastic θ-methods for stochastic delay integro-differential equations. International Journal of Computer Mathematics 88:7, pages 1417-1429.
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Articles from other publishers (19)

Xiaoyue Li, Xuerong Mao & Guoting Song. (2024) An explicit approximation for super-linear stochastic functional differential equations. Stochastic Processes and their Applications 169, pages 104275.
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Jiao Wen & Chengming Huang. (2024) Multistep Runge–Kutta methods for Volterra integro-differential equations. Journal of Computational and Applied Mathematics 436, pages 115384.
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Lin Hu, Aining Chan & Xuezhong Bao. (2021) Numerical analysis of the balanced methods for stochastic Volterra integro-differential equations. Computational and Applied Mathematics 40:6.
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Gui-Lai Zhang. (2020) Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations. Advances in Difference Equations 2020:1.
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Davood Ahmadian & Omid Farkhondeh Rouz. (2020) Exponential mean-square stability of numerical solutions for stochastic delay integro-differential equations with Poisson jump. Journal of Inequalities and Applications 2020:1.
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Gui-Lai Zhang. (2019) Asymptotical stability of numerical methods for semi-linear impulsive differential equations. Computational and Applied Mathematics 39:1.
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Linna Liu, Haoyi Mo & Feiqi Deng. (2019) Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability. Applied Mathematics and Computation 353, pages 320-328.
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Chen Fei, Mingxuan Shen, Weiyin Fei, Xuerong Mao & Litan Yan. (2019) Stability of highly nonlinear hybrid stochastic integro-differential delay equations. Nonlinear Analysis: Hybrid Systems 31, pages 180-199.
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Yu Zhang & Longsuo Li. (2018) Analysis of stability for stochastic delay integro-differential equations. Journal of Inequalities and Applications 2018:1.
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Igor Poloskov & Vladimir Malanin. (2015) A scheme for study of linear stochastic time-delay dynamical systems under continuous and impulsive fluctuations. International Journal of Dynamics and Control 4:2, pages 195-203.
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Qiang Wu, Lin Hu & Zujin Zhang. (2014) Convergence and stability of balanced methods for stochastic delay integro-differential equations. Applied Mathematics and Computation 237, pages 446-460.
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Shifang Kuang, Yunjian Peng, Feiqi Deng & Wenhua Gao. (2013) Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays. Abstract and Applied Analysis 2013, pages 1-11.
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Feng Jiang, Yi Shen & Xiaoxin Liao. (2012) A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations. Journal of Systems Science and Complexity 25:5, pages 873-879.
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Qiyong Li & Siqing Gan. (2011) Mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations. Journal of Applied Mathematics and Computing 39:1-2, pages 69-87.
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Qiyong Li & Siqing Gan. (2012) Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps. Abstract and Applied Analysis 2012, pages 1-13.
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A. Rathinasamy & K. Balachandran. (2011) -stability of the split-step -methods for linear stochastic delay integro-differential equations. Nonlinear Analysis: Hybrid Systems 5:4, pages 639-646.
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Feng Jiang, Yi Shen & Junhao Hu. (2011) Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching. Communications in Nonlinear Science and Numerical Simulation 16:2, pages 814-821.
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Jianguo Tan & Hongli Wang. (2010) Convergence and stability of the split-step backward Euler method for linear stochastic delay integro-differential equations. Mathematical and Computer Modelling 51:5-6, pages 504-515.
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A. Rathinasamy & K. Balachandran. (2008) Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations. Nonlinear Analysis: Hybrid Systems 2:4, pages 1256-1263.
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