Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method
Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method
复制标题
超越龙格-库塔-温策尔-克莱默斯-布里渊方法
作者：
J. Bamber;Will Handley
研究了一阶常微分方程组高振动解的Runge-Kutta-Wentzel-Kramers-Brillouin方法的高维推广。这种方法可以提高用于计算爱因斯坦-玻尔兹曼方程数值解的程序的性能和适应性。我们在爱因斯坦-玻尔兹曼方程上测试了基于Magnus展开的方法，用于一个简单的宇宙模型，该模型由带有少量冷暗物质的光子主导。与标准龙格-库塔积分方法相比，Magnus展开方法的运行速度提高了约50%。从Magnus展开和Wentzel-Kramers-Brillouin(WKB)方法得到的近似解的比较表明，这两种方法是不同的数学方法。与WKB相比，简单的Magnus扩展解决方案显示出较差的远程精度。然而，我们也演示了如何改进标准的Magnus方法以获得新的“Jordan-Magnus”方法。这在简单的二维系统上具有类似WKB的性能，尽管它的高维泛化仍然难以捉摸。
We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve the performance and adaptability of the codes which are used to compute numerical solutions to the Einstein-Boltzmann equations. We test Magnus expansion-based methods on the Einstein-Boltzmann equations for a simple universe model dominated by photons with a small amount of cold dark matter. The Magnus expansion methods achieve an increase in run speed of about 50% compared to a standard Runge-Kutta integration method. A comparison of approximate solutions derived from the Magnus expansion and the Wentzel-Kramers-Brillouin (WKB) method implies the two are distinct mathematical approaches. Simple Magnus expansion solutions show inferior long range accuracy compared to WKB. However we also demonstrate how one can improve on the standard Magnus approach to obtain a new "Jordan-Magnus" method. This has a WKB-like performance on simple two-dimensional systems, although its higher-dimensional generalization remains elusive.
DOI：
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发表时间：
2015-06
期刊：
Journal of nature and science
影响因子：
--
作者：
E. Mananga;J. Moghaddasi;A. Sana;A. Akinmoladun;M. Sadoqi
通讯作者：
E. Mananga;J. Moghaddasi;A. Sana;A. Akinmoladun;M. Sadoqi
求解高振荡常微分方程的有效方法及其在物理系统中的应用
影响因子：
4.2
作者：
Agocs F
通讯作者：
Agocs F