A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
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TLDR
A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrodinger equation and it is proved that the optimal rate of convergence is in the order of O in the discrete L 2 norm without any restrictions on the grid ratio.About:
This article is published in Journal of Computational Physics.The article was published on 2017-01-01 and is currently open access. It has received 112 citations till now. The article focuses on the topics: Split-step method & Spectral method.read more
Citations
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Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
TL;DR: This work designs and analyzes a class of up to fourth order maximum principle preserving integrators for the Allen-Cahn equation and proves that the proposed method is convergent with order O ( τ p + h 2 ) in the discrete L ∞ norm.
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Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation
TL;DR: In this paper, the authors proposed the conservative linearized Galerkin finite element methods (FEMs) for the nonlinear Klein-Gordon-Schrodinger equation (KGSE) with homogeneous boundary conditions.
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Mass- and energy-preserving exponential Runge–Kutta methods for the nonlinear Schrödinger equation
TL;DR: A family of arbitrarily high-order structure-preserving exponential Runge–Kutta methods are developed for the nonlinear Schrodinger equation by combining the scalar auxiliary variable approach with the exponential Run Geometric method.
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Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrödinger equation
TL;DR: These two FPS methods are proved to be spectrally accurate in space and second-order accurate in time, respectively and to preserve the total mass and energy in the discrete sense by introducing a modified mass functional and a modified energy functional.
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Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: A unified framework
TL;DR: In this article, a unified framework for conforming and non-conforming virtual element methods for nonlinear Schrodinger equation is presented, in which the authors prove the boundedness, unique solvability and optimal convergence of the conforming VM scheme.
References
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