Monotonic Bicompact Schemes for Linear Transport Equations

B. V. Rogov; M. N. Mikhailovskaya

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Monotonic Bicompact Schemes for Linear Transport Equations

机译：线性传输方程的单调双紧格式

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The biocompact difference scheme earlier proposed by these authors for a linear transport equation, which has the fourth-order approximation in spatial coordinate on the two-point stencil and the first-order approximation in time, is monotonic. This implicit scheme is absolutely stable and can be solved by explicit formulas of a running calculation. On the basis of this scheme a monotone non- linear homogeneous difference scheme of high (third for smooth solutions) order accuracy in time is constructed. Calculations of test problems with discontinuous solutions have demonstrated that the proposed scheme has a significant advantage in accuracy over the known nonoscillatory schemes of high-order approximation.

机译：这些作者较早提出的关于线性输运方程的生物紧致差分方案是单调的，该线性运输方程在两点模板上具有空间坐标的四阶近似和时间的一阶近似。这种隐式方案是绝对稳定的，可以通过运行中的计算公式来解决。在此方案的基础上，构造了单调非线性齐次差分方案，该方案在时间上具有较高的阶次精度（对于光滑解，则为第三阶）。不连续解的测试问题的计算表明，与已知的高阶近似非振荡方案相比，所提出的方案在准确性方面具有显着优势。

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《Mathematical models and computer simulations》 |2012年第1期|共9页
作者
B. V. Rogov; M. N. Mikhailovskaya;
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正文语种 eng
中图分类数学;
关键词
transport equation; bicompact difference schemes; monotonicity;

机译：输运方程;双紧差分格式;单调性;

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1. Monotonic Bicompact Schemes for Linear Transport Equations [J] . B. V. Rogov, M. N. Mikhailovskaya Mathematical models and computer simulations . 2012,第1期

机译：线性传输方程的单调双紧格式
2. Bicompact scheme for the multidimensional stationary linear transport equation [J] . E.N. Aristova, B.V. Rogov Applied numerical mathematics . 2015,第jula期

机译：多维平稳线性传输方程的双紧方案
3. Bicompact Schemes for an Inhomogeneous Linear Transport Equation in the Case of a Large Optical Depth [J] . E. N. Aristova Mathematical models and computer simulations . 2014,第3期

机译：大光学深度情况下非均匀线性传输方程的双紧格式
4. General Theory of Linear Functional Equations in the Space of Strictly Monotonic Functions [C] . Jitka Laitochová International Conference on Difference Equations and Applications . 2010

机译：严格单调函数空间中线性函数方程的一般理论
5. Existence of bounded monotonic solutions of second order nonlinear differential equations. [D] . Ballinger, Jeff. 2009

机译：二阶非线性微分方程有界单调解的存在性。
6. A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme [O] . Ulf-Peter Hansen, Oliver Rauh, Indra Schroeder 2016

机译：建立具有大量状态的离子传输的循环和线性反应方案的通量方程的简单方法：箭头方案
7. Two variants of parallel implementation of high-order accurate bicompact schemes for multi-dimensional inhomogeneous transport equation [O] . Aleksandr Viktorovich Chikitkin, Boris Vadimovich Rogov 2018

机译：用于多维不均匀传输方程的高阶精确二聚处理方案的两次平行实施的两个变体

Monotonic Bicompact Schemes for Linear Transport Equations

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