求解非线性退化抛物方程的HWENO-LW格式
HWENO-LW Scheme for Solving Nonlinear Degenerate Parabolic Equations
摘要: 本文构造了基于Lax-Wendroff时间离散的有限差分HWENO (Hermite加权本质非振荡)格式，用于求解非线性退化抛物方程。与传统的Runge-Kutta时间离散方法相比，Lax-Wendroff方法在提高计算效率的同时，能够在解的光滑区域实现时空一致的高阶精度。通过数值算例，验证了该方法的有效性。
Abstract: This paper constructs a finite difference HWENO (Hermite Weighted Essentially Non-Oscillatory) scheme based on Lax-Wendroff time discretization for solving nonlinear degenerate parabolic equations. Compared to traditional Runge-Kutta time discretization methods, the Lax-Wendroff method improves computational efficiency while achieving high-order accuracy in both space and time in smooth regions of the solution. The effectiveness of the method is validated through numerical examples.
文章引用：孔莹莹, 刘红霞. 求解非线性退化抛物方程的HWENO-LW格式[J]. 应用数学进展, 2025, 14(3): 292-302. https://doi.org/10.12677/aam.2025.143116

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