论文标题
具有时间依赖系数的三阶方程的数值研究：KDVB方程
A numerical study of third-order equation with time-dependent coefficients: KdVB equation
论文作者
论文摘要
在本文中，我们介绍了具有非周期性边界条件和时间依赖性系数的三阶微分方程的数值分析，即线性korteweg-de vries burgers方程。由于政府这种方程式的分散和耗散现象，这种数值分析是动机的。这项工作基于以前具有恒定系数的分散方程的方法，扩展了字段，以包括新的方程式，到目前为止，该方程已经避免了时间不断发展的参数。更确切地说，在整个Legendre-Petrov-Galerkin方法中，我们证明了在适当的加权Sobolev空间中近似的稳定性和收敛结果。这些结果允许将这些时间参数的作用和权衡。之后，我们从数值上研究了几个概况的分散分散关系，进一步提供了对实施方法的见解，该方法允许表现出我们的数值算法的准确性和效率。
In this article we present a numerical analysis for a third-order differential equation with non-periodic boundary conditions and time-dependent coefficients, namely, the linear Korteweg-de Vries Burgers equation. This numerical analysis is motived due to the dispersive and dissipative phenomena that government this kind of equations. This work builds on previous methods for dispersive equations with constant coefficients, expanding the field to include a new class of equations which until now have eluded the time-evolving parameters. More precisely, throughout the Legendre-Petrov-Galerkin method we prove stability and convergence results of the approximation in appropriate weighted Sobolev spaces. These results allow to show the role and trade off of these temporal parameters into the model. Afterwards, we numerically investigate the dispersion-dissipation relation for several profiles, further provide insights into the implementation method, which allow to exhibit the accuracy and efficiency of our numerical algorithms.
