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- Title
RICHARDSON EXTRAPOLATION OF THE CRANK-NICOLSON SCHEME FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS.
- Authors
YAFEI XU; WEIDONG ZHAO
- Abstract
In this work, we consider Richardson extrapolation of the Crank-Nicolson (CN) scheme for backward stochastic differential equations (BSDEs). First, applying the Adomian decomposition to the nonlinear generator of BSDEs, we introduce a new system of BSDEs. Then we theoretically prove that the solution of the CN scheme for BSDEs admits an asymptotic expansion with its coefficients the solutions of the new system of BSDEs. Based on the expansion, we propose Richardson extrapolation algorithms for solving BSDEs. Finally, some numerical tests are carried out to verify our theoretical conclusions and to show the stability, efficiency and high accuracy of the algorithms.
- Subjects
RICHARDSON (Tex.); EXTRAPOLATION; ASYMPTOTIC expansions; STOCHASTIC differential equations; ALGORITHMS
- Publication
International Journal of Numerical Analysis & Modeling, 2024, Vol 21, Issue 2, p268
- ISSN
1705-5105
- Publication type
Article
- DOI
10.4208/ijnam2024-1011