关于差分格式的稳定性。带源项的双曲型守恒律的中心格式
On stability of difference schemes. Central schemes for hyperbolic conservation laws with source terms
摘要：
研究了一般双曲型守恒律方程组带源项差分格式的稳定性。其基本方法是用相应的变分格式来研究非线性格式的稳定性。这种方法导致应用线性方程系统的稳定性理论来建立相应的非线性方案的稳定性。建立了非线性格式稳定的充要条件是相应的变分格式稳定。对中心Lax-Friedrichs（LxF）格式进行了二阶精度的改进。在中心格式中使用单调分段三次插值来精确逼近模型。研究了改进格式的稳定性。一些版本的修改后的计划进行了测试的几个守恒律，该计划被发现是准确和强大的。对于一般具有刚性源项的双曲型守恒律方程，基于算子分裂技术构造了一个二阶非交错中心格式。
英文摘要：
The stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability of a non-linear scheme in terms of its cor- responding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability of the corresponding non-linear scheme. It is established the notion that a non-linear scheme is stable if and only if the corresponding scheme in variations is stable. A new modification of the central Lax-Friedrichs (LxF) scheme is developed to be of the second order accuracy. A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The stability of the modified scheme are investigated. Some versions of the modified scheme are tested on several conservation laws, and the scheme is found to be accurate and robust. As applied to hyperbolic conservation laws with, in general, stiff source terms, it is constructed a second order nonstaggered central scheme based on operator-splitting techniques.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
