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Hybrid spline difference method for the Burgers' equation

机译：Burgers方程的混合样条差法

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摘要

This study developed a high accuracy hybrid spline difference method, and deduced a difference equation that is very similar to finite difference method from the concept of spline difference. As validated by nonlinear Burgers' equation, the concept of difference made the computational process as simple as the finite difference method, and easy to be implemented. The free parameters α → 1/12 and α → 1/6 were combined in the concept of spline hybrid, in order to increase the accuracy of the first and second derivatives of space from O(h ~2) of finite difference method to the O(h ~4). The accuracy was improved, and the numerical oscillation with the increase in parameter R _e was improved greatly.
机译：本研究提出了一种高精度的混合样条差法，并从样条差的概念推导了一个与有限差分法非常相似的差分方程。通过非线性Burgers方程验证，差分的概念使计算过程像有限差分法一样简单，并且易于实现。在样条混合的概念中将自由参数α→1/12和α→1/6组合在一起，以提高从有限差分法的O（h〜2）到空间的一阶和二阶导数的精度。 O（h〜4）。精度得到了改善，并且随着参数R _e的增加，数值振荡得到了极大的改善。

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