具有最优混合的混合三次-有理半拉格朗日方法
Hybrid-Cubic-Rational Semi-Lagrangian Method with the Optimal Mixing
AI总结：
本文提出一种混合三次-有理插值的半拉格朗日方法，通过理论最优比例混合三次与有理函数，兼顾高精度与凸性保持，并数值验证其有效性。
摘要：
本文介绍了一种用于平流方程的混合三次-有理插值的半拉格朗日方法。在该方法中，物理量的空间分布由三次函数和有理函数的组合进行插值。为了同时实现高精度和解的凸性保持，这两个函数以理论上给出的最优比例进行混合。通过一些数值实验验证了该方法的精度和有效性。
英文摘要：
A semi-Lagrangian method for advection equation with hybrid cubic-rational interpolation is introduced. In the present method, the spatial profile of physical quantities is interpolated with a combination of a cubic and a rational function. For achieving both high accuracy and convexity preserving of solution, the two functions are mixed in the optimal ratio which is given theoretically. Accuracy and validity of this method is demonstrated with some numerical experiments.
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。
