论文标题
特征向量分解以确定抛物线PDE中数值振荡的存在，形状和位置
Eigenvector decomposition to determine the existence, shape, and location of numerical oscillations in Parabolic PDEs
论文作者
论文摘要
在本文中，我们采用了线性代数和功能分析来确定无振荡和稳定的解决方案的必要条件，以实现线性和非线性抛物线偏微分方程。我们将奇异值分解和傅立叶分析应用于各种有限差异方案，以在本征函数（由特征向量取样）及其特征光谱的形状中提取模式。通过这些，我们确定了初始条件和边界条件如何影响数值振荡的频率和长期行为，以及对它们最敏感的解决方案区域的位置。
In this paper, we employed linear algebra and functional analysis to determine necessary and sufficient conditions for oscillation-free and stable solutions to linear and nonlinear parabolic partial differential equations. We applied singular value decomposition and Fourier analysis to various finite difference schemes to extract patterns in the eigenfunctions (sampled by the eigenvectors) and the shape of their eigenspectrum. With these, we determined how the initial and boundary conditions affect the frequency and long term behavior of numerical oscillations, as well as the location of solution regions most sensitive to them.
