Multiple relaxation exponential Runge-Kutta methods for the nonlinear Schrödinger equation (Q6658285)

scientific article; zbMATH DE number 7963013

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English	Multiple relaxation exponential Runge-Kutta methods for the nonlinear Schrödinger equation	scientific article; zbMATH DE number 7963013

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instance of

scholarly article

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title

Multiple relaxation exponential Runge-Kutta methods for the nonlinear Schrödinger equation (English)

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SIAM Journal on Numerical Analysis

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publication date

8 January 2025

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zbMATH Keywords

relaxation technique

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exponential Runge-Kutta methods

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structure-preserving methods

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high-order accuracy

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nonlinear Schrödinger equation

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Structure-preserving Gauss methods for the nonlinear Schrödinger equation

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High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations

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Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations

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Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

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High-Order Mass- and Energy-Conserving Methods for the Nonlinear Schrödinger Equation

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A Relaxation Scheme for the Nonlinear Schrödinger Equation

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Energy-preserving methods for nonlinear Schrödinger equations

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Gaussons: Solitons of the Logarithmic Schrödinger Equation

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Multiple-relaxation Runge Kutta methods for conservative dynamical systems

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Line Integral Methods for Conservative Problems

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Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)

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Solitons in Laser Physics

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Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime

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On the Preservation of Invariants by Explicit Runge--Kutta Methods

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A new Lagrange multiplier approach for gradient flows

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Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows

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Stability of Runge-Kutta Methods for Trajectory Problems

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Q3687624

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Explicit methods based on a class of four stage fourth order Runge-Kutta methods for preserving quadratic laws

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Finite-difference solutions of a non-linear Schrödinger equation

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Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis

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Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation

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Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes

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Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme

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High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation

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Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations

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Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models

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Time integration and discrete Hamiltonian systems

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Q4321926

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Mass-, Energy-, and Momentum-Preserving Spectral Scheme for Klein-Gordon-Schrödinger System on Infinite Domains

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Q2960810

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Geometric Numerical Integration

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Solving Ordinary Differential Equations I

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Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation

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Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations

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Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection

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Additive Runge-Kutta schemes for convection-diffusion-reaction equations

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Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms

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Invariants preserving schemes based on explicit Runge-Kutta methods

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A Semi-implicit Exponential Low-Regularity Integrator for the Navier--Stokes Equations

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Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems

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Relaxation exponential Runge-Kutta methods and their applications to semilinear dissipative/conservative systems

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Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs

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Linearly implicit and high-order energy-preserving relaxation schemes for highly oscillatory Hamiltonian systems

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High-order Lagrange multiplier method for the coupled Klein-Gordon-Schrödinger system

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Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems

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Some new additive Runge-Kutta methods and their applications

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Geometric integration using discrete gradients

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Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems

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A new class of energy-preserving numerical integration methods

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Relaxation Runge-Kutta methods for Hamiltonian problems

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General relaxation methods for initial-value problems with application to multistep schemes

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Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations

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A General Framework of Low Regularity Integrators

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Methods for the Numerical Solution of the Nonlinear Schroedinger Equation

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A method for the integration in time of certain partial differential equations

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The scalar auxiliary variable (SAV) approach for gradient flows

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A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

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Efficient implementation of essentially nonoscillatory shock-capturing schemes

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Local discontinuous Galerkin methods for nonlinear Schrödinger equations

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