Numerical Integration of stochastic differential equations: The Heun Algorithm Revisited and Itô-Stratonovich Calculus
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909753461964800 |
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| author | Mannella, Riccardo |
| author_facet | Mannella, Riccardo |
| contents | The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and equilibrium properties of these alternatives are assessed through extensive numerical simulations. Our results confirm that the standard Heun scheme remains a benchmark integration algorithm for SDEs due to its robust performance. As a byproduct of this analysis, we also disprove a previous claim in the literature regarding the strong convergence of the Heun scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Integration of stochastic differential equations: The Heun Algorithm Revisited and Itô-Stratonovich Calculus Mannella, Riccardo Numerical Analysis Disordered Systems and Neural Networks Statistical Mechanics The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and equilibrium properties of these alternatives are assessed through extensive numerical simulations. Our results confirm that the standard Heun scheme remains a benchmark integration algorithm for SDEs due to its robust performance. As a byproduct of this analysis, we also disprove a previous claim in the literature regarding the strong convergence of the Heun scheme. |
| title | Numerical Integration of stochastic differential equations: The Heun Algorithm Revisited and Itô-Stratonovich Calculus |
| topic | Numerical Analysis Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2508.19040 |