Numerical solution of nonlinear Schrödinger equation with damping term on unbounded domain
Numerical solution of nonlinear Schrödinger equation with damping term on unbounded domain
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DOI：
10.1016/j.aml.2023.108893
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发表时间：
2023-10
期刊：
影响因子：
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通讯作者：
Hongwei Li;Lulu Chen
中科院分区：
文献类型：
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作者：
Hongwei Li;Lulu Chen
应用人工边界法数值求解无界区域上带阻尼项的非线性薛定谔方程。提出了一种新的变换，消除了人工边界条件设计中的阻尼项。基于算子分裂方法的思想，研究了人工边界条件，将原问题转化为初边值问题。通过能量估计分析了简化问题的稳定性。数值算例验证了该方法的准确性和有效性。
The artificial boundary method is applied to numerically solve the nonlinear Schrödinger equation with damping term on unbounded domain. A novel transformation is developed to eliminate the troublesome damping term, which yields the difficulty to design the artificial boundary conditions. The artificial boundary conditions are investigated to reduce the original problem into an initial boundary value problem, based on the idea of operator splitting approach. The stability of the reduced problem is analyzed by the energy estimation. The accuracy and effectiveness of the proposed method are verified by numerical examples.