用于后向随机微分方程的理查森外推法克兰克-尼科尔森方案

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2024-04-01 DOI:10.4208/ijnam2024-1011

Yafei Xu, Weidong Zhao

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引用次数: 0

摘要

在这项研究中，我们考虑了针对后向随机微分方程（BSDEs）的克兰克-尼科尔森（CN）方案的理查德森外推法。首先，我们将 Adomiandecomposition 应用于 BSDEs 的非线性生成器，引入了一个新的 BSDEs 系统。然后，我们从理论上证明了 BSDEs 的 CN 方案的解允许一个渐近展开，其系数就是新的 BSDEs 系统的解。基于该展开，我们提出了求解 BSDE 的理查森外推法算法。最后，我们进行了一些数值试验来验证我们的理论结论，并展示了算法的稳定性、高效性和高精确度。

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Richardson Extrapolation of the Crank-Nicolson Scheme for Backward Stochastic Differential Equations

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.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.