关于带对流的拟线性PDAEs：应用、指数、数值解
On quasi-linear PDAEs with convection: applications, indices, numerical solution
AI总结：
针对一类包含对流非线性项的拟线性偏微分代数方程，提出确定时间和空间指数的方法，并基于有限差分分裂过程（改进的分步法与矩阵分解耦合）求解初边值问题，证明收敛性并给出等离子体物理应用中的数值结果。
摘要：
对于一类包含对流型非线性项的拟线性偏微分代数方程，考虑确定时间和空间指数的可能性。作为一个典型例子，我们研究等离子体物理中的应用。特别地，我们通过相应的有限差分分裂过程讨论初边值问题的数值解，该过程是著名的分步法与矩阵分解耦合的改进。研究了数值解向相应初边值问题精确解的收敛性。给出了等离子体PDAE数值解的一些结果。
英文摘要：
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an application from plasma physics. Especially we discuss the numerical solution of initial boundary value problems by means of a corresponding finite difference splitting procedure which is a modification of a well known fractional step method coupled with a matrix factorization. The convergence of the numerical solution towards the exact solution of the corresponding initial boundary value problem is investigated. Some results of a numerical solution of the plasma PDAE are given.
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