Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913043181469696 |
|---|---|
| author | Wang, Yibo Cao, Wanrong Cao, Yanzhao |
| author_facet | Wang, Yibo Cao, Wanrong Cao, Yanzhao |
| contents | The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the continuous problem in space, we utilize a spectral Galerkin method. Subsequently, we introduce a nonlinear-tamed exponential integrator scheme, resulting in a fully discrete scheme. Within the framework of semigroup theory, this study provides precise estimations of the Sobolev regularity, $L^\infty$ regularity in space, and Hölder continuity in time for the mild solution, as well as for its semi-discrete and full-discrete approximations. Building upon these results, we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions. A numerical example is presented to validate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation Wang, Yibo Cao, Wanrong Cao, Yanzhao Numerical Analysis 60H35, 65C30, 60H15 The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the continuous problem in space, we utilize a spectral Galerkin method. Subsequently, we introduce a nonlinear-tamed exponential integrator scheme, resulting in a fully discrete scheme. Within the framework of semigroup theory, this study provides precise estimations of the Sobolev regularity, $L^\infty$ regularity in space, and Hölder continuity in time for the mild solution, as well as for its semi-discrete and full-discrete approximations. Building upon these results, we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions. A numerical example is presented to validate the theoretical findings. |
| title | Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation |
| topic | Numerical Analysis 60H35, 65C30, 60H15 |
| url | https://arxiv.org/abs/2408.00947 |