NUMERICAL STABILITY OF HEUN METHODS FOR NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
Wang Wenqiang1,2, Chen Yanping3
1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China;
2. Civil Engineering & Machanics College, Xiangtan University, Xiangtan 411105, Hunan, China;
3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
In this paper, the authors investigated the numerical stability of Heun methods for nonlinear stochastic delay differential equations. When the analytical solution satisfies the conditions of mean-square stability, and if the drift term satisfy some restrictions, then the Heun methods with linear interpolation procedure is exponential mean-square stable and GMS-stable, the Heun methods is mean-square stable(MS-stable). Moreover, these results are also verified by some numerical examples.
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