Year: 2023
Author: Qiang Han, Shaolin Ji
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 287–304
Abstract
In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2112-m2019-0289
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 287–304
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Backward stochastic differential equation Stochastic linear two-step scheme Local truncation error Stability and convergence.
Author Details
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Novel multi-step predictor–corrector schemes for backward stochastic differential equations
Han, Qiang
Ji, Shaolin
Communications in Nonlinear Science and Numerical Simulation, Vol. 139 (2024), Iss. P.108269
https://doi.org/10.1016/j.cnsns.2024.108269 [Citations: 0]