Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in $L^p$-sense
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912069774737408 |
|---|---|
| author | Nguyen, Tuan Anh |
| author_facet | Nguyen, Tuan Anh |
| contents | We prove that multilevel Picard approximations are capable of approximating solutions of semilinear heat equations in $L^{p}$-sense, ${p}\in [2,\infty)$, in the case of gradient-dependent, Lipschitz-continuous nonlinearities, in the sense that the computational effort of the multilevel Picard approximations grow at most polynomially in both the dimension $d$ and the reciprocal $1/ε$ of the prescribed accuracy $ε$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in $L^p$-sense Nguyen, Tuan Anh Numerical Analysis Analysis of PDEs 65C99, 68T05 We prove that multilevel Picard approximations are capable of approximating solutions of semilinear heat equations in $L^{p}$-sense, ${p}\in [2,\infty)$, in the case of gradient-dependent, Lipschitz-continuous nonlinearities, in the sense that the computational effort of the multilevel Picard approximations grow at most polynomially in both the dimension $d$ and the reciprocal $1/ε$ of the prescribed accuracy $ε$. |
| title | Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in $L^p$-sense |
| topic | Numerical Analysis Analysis of PDEs 65C99, 68T05 |
| url | https://arxiv.org/abs/2410.00203 |