Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916944632872960 |
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| author | Liu, Zhihui Wang, Xiaojie Wu, Xiaoming Zhang, Xiaoyan |
| author_facet | Liu, Zhihui Wang, Xiaojie Wu, Xiaoming Zhang, Xiaoyan |
| contents | A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems. Under a non-contractive condition, we establish a non-asymptotic error bound between the law of the numerical approximation and the target distribution in Wasserstein-1 ($\mathcal{W}_1$) distance through a time-independent weak convergence rate for the proposed schemes. As a by-product of this weak error estimate, we obtain an $\mathcal{O}(τ|\ln τ|)$ convergence rate between the exact and numerical invariant measures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs Liu, Zhihui Wang, Xiaojie Wu, Xiaoming Zhang, Xiaoyan Numerical Analysis 60H35, 37M25, 65C30 A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems. Under a non-contractive condition, we establish a non-asymptotic error bound between the law of the numerical approximation and the target distribution in Wasserstein-1 ($\mathcal{W}_1$) distance through a time-independent weak convergence rate for the proposed schemes. As a by-product of this weak error estimate, we obtain an $\mathcal{O}(τ|\ln τ|)$ convergence rate between the exact and numerical invariant measures. |
| title | Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs |
| topic | Numerical Analysis 60H35, 37M25, 65C30 |
| url | https://arxiv.org/abs/2509.08410 |