求解二维变系数G-方程的高精度交替方向隐格式
High Accuracy Alternating Direction Implicit Scheme for Solving Two-Dimensional Variable Coefficient G-Equations
摘要: 本文提出了求解二维变系数G方程的高精度交替方向隐式(ADI)格式，该方法在物理、金融和计算数学中具有重要应用。我们分析了该格式的稳定性，并进行了数值实验，比较了不同格式的绝对误差，验证了ADI格式的有效性。
Abstract: In this paper, we propose high-accuracy Alternating Direction Implicit (ADI) scheme for solving two-dimensional variable coefficient G-equations, which have significant applications in physics, finance and computational mathematics. The stability of the scheme is analyzed, and numerical experiment is conducted to compare absolute errors across different schemes, confirming the effectiveness of the scheme.
文章引用：张宇, 许乾海, 李洋. 求解二维变系数G-方程的高精度交替方向隐格式[J]. 理论数学, 2025, 15(2): 268-276. https://doi.org/10.12677/pm.2025.152067

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