Volume 7, Issue 3
Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations

Liming Liao, Guanghua Ji, Zhongwei Tang & Hui Zhang

East Asian J. Appl. Math., 7 (2017), pp. 566-582.

Published online: 2018-02

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  • Abstract

An adaptive finite element method is adopted to simulate the steady state coupled Schrödinger equations with a small parameter. We use damped Newton iteration to solve the nonlinear algebraic system. When the solution domain is elliptic, our numerical results with Dirichlet or Neumann boundary conditions are consistent with previous theoretical results. For the dumbbell and circular ring domains with Dirichlet boundary conditions, we obtain some new results that may be compared with future theoretical analysis.

  • Keywords

Schrödinger equations, damped Newton iteration, adaptive finite element method, spike-layer solution.

  • AMS Subject Headings

33F05, 68U20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-566, author = {}, title = {Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {566--582}, abstract = {

An adaptive finite element method is adopted to simulate the steady state coupled Schrödinger equations with a small parameter. We use damped Newton iteration to solve the nonlinear algebraic system. When the solution domain is elliptic, our numerical results with Dirichlet or Neumann boundary conditions are consistent with previous theoretical results. For the dumbbell and circular ring domains with Dirichlet boundary conditions, we obtain some new results that may be compared with future theoretical analysis.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030616.130517a}, url = {http://global-sci.org/intro/article_detail/eajam/10765.html} }
TY - JOUR T1 - Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations JO - East Asian Journal on Applied Mathematics VL - 3 SP - 566 EP - 582 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.030616.130517a UR - https://global-sci.org/intro/article_detail/eajam/10765.html KW - Schrödinger equations, damped Newton iteration, adaptive finite element method, spike-layer solution. AB -

An adaptive finite element method is adopted to simulate the steady state coupled Schrödinger equations with a small parameter. We use damped Newton iteration to solve the nonlinear algebraic system. When the solution domain is elliptic, our numerical results with Dirichlet or Neumann boundary conditions are consistent with previous theoretical results. For the dumbbell and circular ring domains with Dirichlet boundary conditions, we obtain some new results that may be compared with future theoretical analysis.

Liming Liao, Guanghua Ji, Zhongwei Tang & Hui Zhang. (2020). Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations. East Asian Journal on Applied Mathematics. 7 (3). 566-582. doi:10.4208/eajam.030616.130517a
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