论文标题
实际线上的分数schrödinger方程的有效光谱方法
An efficient spectral method for the fractional Schrödinger equation on the real line
论文作者
论文摘要
实际线路上的分数Schrödinger方程（FSE）是在广泛的物理环境中出现的，由于非本地性质和无穷大的溶液的功率定律衰减，它们的数值模拟具有挑战性。在本文中，我们提出了一种基于恶质 - 塔克纳克函数的空间中FSE的新光谱离散方案。我们表明，在基础FSE涉及Laplacian的平方根的情况下，这种新的离散方案的性能要比现有的离散方案要好得多，而在其他情况下，它也表现出可比性甚至更好的性能。提供了数值实验来说明所提出方法的有效性。
The fractional Schrödinger equation (FSE) on the real line arises in a broad range of physical settings and their numerical simulation is challenging due to the nonlocal nature and the power law decay of the solution at infinity. In this paper, we propose a new spectral discretization scheme for the FSE in space based upon Malmquist-Takenaka functions. We show that this new discretization scheme achieves much better performance than existing discretization schemes in the case where the underlying FSE involves the square root of the Laplacian, while in other cases it also exhibits comparable or even better performance. Numerical experiments are provided to illustrate the effectiveness of the proposed method.
