Kadomtsev-Petviashvili方程的分裂方法
A splitting approach for the Kadomtsev--Petviashvili equation
摘要：
我们认为分裂方法的Kadomtsev-Petviashvili方程的周期性边界条件，并表明，必要的插值过程可以有效地实现。将该数值方案产生的误差与Klein和Roidot（SIAM J. Sci.计算：2011）对Kadomtsev-Petviashvili方程的刚性解表现最好。由于许多经典的高阶分裂方法不能很好地执行，我们提出了一个稳定的外推方法，以构建一个有效的四阶数值格式。此外，守恒性质和可能的降低的考虑中的数值格式的某些初始值的订单。
英文摘要：
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev--Petviashvili equation. Since many classic high order splitting methods do not perform well, we propose a stable extrapolation method in order to construct an efficient numerical scheme of order four. In addition, the conservation properties and the possibility of order reduction for certain initial values for the numerical schemes under consideration is investigated.
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