1. Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model.
- Author
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Yang, Xiaochen, Li, Mengna, Yang, Zhanwen, and Zhang, Chiping
- Subjects
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WIENER processes , *EULER method , *STOCHASTIC processes , *STOCHASTIC models , *NUMERICAL analysis , *NONLINEAR dynamical systems - Abstract
The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIS model. Compared with the existing numerical methods, a linearly backward Euler method with truncated Wiener process is introduced with a less computational cost and a better dynamic behavior. We discuss the numerical positivity by the truncated Wiener process, which is the basis for the investigation of convergence and dynamic behavior. The numerical dynamical behaviors (extinction and persistence) are obtained by an exponential representation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIS model. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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