Numerical Computations of Nonlocal Schrodinger Equations on the Real Line

• 作者: Chunxiong Zheng Jiwei Zhang Yonggui Yan
• 来源期刊: 应用数学与计算数学学报(英文)
• 学科: 数学
• 关键词: Nonrefecting boundary conditions Artifcial boundary method Nonlocal Schrödinger equation Z-TRANSFORM Nonlocal models
• 年，卷（期）: 2020,（2）
• 页码范围: 241-260
• 页数: 20页
• 分类号: O17

摘要

The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.