不定常系数三阶方程：KdVB方程的数值研究
A numerical study of third-order equation with time-dependent coefficients: KdVB equation
摘要：
本文对一类具有非周期边界条件和不定常系数的三阶微分方程，即线性Korteweg-de Vries Burgers方程进行了数值分析.这种数值分析的动机是由于色散和耗散现象，政府这类方程。这项工作建立在以前的色散方程的方法与常系数，扩大领域，包括一类新的方程，到目前为止，已经逃避了随时间变化的参数。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索伯列夫空间的逼近的稳定性和收敛结果。这些结果可以显示这些时间参数到模型中的作用和权衡。之后，我们数值研究了几个配置文件的色散-耗散关系，进一步提供见解的实现方法，这允许展示我们的数值算法的准确性和效率。
英文摘要：
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.
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