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求解非线性退化抛物方程的HWENO-LW格式
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Abstract:
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。
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.
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