Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913157452136448 |
|---|---|
| author | Fang, Shuixin Qiu, Yue Zhao, Weidong |
| author_facet | Fang, Shuixin Qiu, Yue Zhao, Weidong |
| contents | The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet been well established for backward stochastic differential equations (BSDEs) -- motivating the current work to address this gap. Specifically, we propose a new class of explicit Runge-Kutta schemes for BSDEs. These schemes admit a concise formulation that closely mirrors their ODE counterparts. Building on this formulation, we extend the Butcher theory to the proposed schemes, thereby enabling a symbolic derivation of Taylor expansions for the local truncation errors, and yielding the order conditions. Our approach preserves the elegance and generality of the original Butcher theory: it avoids stage-by-stage error expansions and provides a systematic, stage-inductive analysis, applicable to schemes with any number of stages and any target order. Numerical experiments support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations Fang, Shuixin Qiu, Yue Zhao, Weidong Numerical Analysis 65C30, 60H35, 65C20 The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet been well established for backward stochastic differential equations (BSDEs) -- motivating the current work to address this gap. Specifically, we propose a new class of explicit Runge-Kutta schemes for BSDEs. These schemes admit a concise formulation that closely mirrors their ODE counterparts. Building on this formulation, we extend the Butcher theory to the proposed schemes, thereby enabling a symbolic derivation of Taylor expansions for the local truncation errors, and yielding the order conditions. Our approach preserves the elegance and generality of the original Butcher theory: it avoids stage-by-stage error expansions and provides a systematic, stage-inductive analysis, applicable to schemes with any number of stages and any target order. Numerical experiments support the theoretical results. |
| title | Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations |
| topic | Numerical Analysis 65C30, 60H35, 65C20 |
| url | https://arxiv.org/abs/2508.18707 |