Symplectic schemes for linear stochastic Schrödinger equations with variable coefficients

DOI10.1155/2014/427023zbMath1470.65178OpenAlexW1974963288WikidataQ59037949 ScholiaQ59037949MaRDI QIDQ1724105

Xiuling Yin, Yanqin Liu

Publication date: 14 February 2019

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/427023

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Time-dependent Schrödinger equations and Dirac equations (35Q41) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Cites Work

• Finite difference method for the reverse parabolic problem
• An efficient higher order compact scheme to capture heat transfer solutions in spherical geometry
• High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
• Numerical solution of fuzzy differential equations under generalized differentiability
• Compact finite difference schemes with spectral-like resolution
• Coercive solvability of the nonlocal boundary value problem for parabolic differential equations
• Multisymplecticity of the centred box discretization for Hamiltonian PDEs with \(m\geq 2\) space dimensions
• Efficient numerical algorithms for the solution of ``good Boussinesq equation in water wave propagation
• Fite-Wintner-Leighton-type oscillation criteria for second-order differential equations with nonlinear damping
• New wavelets collocation method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds
• Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term
• Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients
• Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
• Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation
• Geometric Numerical Integration
• Symplectic methods for the nonlinear Schrödinger equation
• Numerical simulation of focusing stochastic nonlinear Schrödinger equations

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