A symmetric low-regularity integrator for nonlinear Klein-Gordon equation
DOI10.1090/mcom/3751zbMath1498.65178OpenAlexW4224022239MaRDI QIDQ5097374
Publication date: 23 August 2022
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/mcom/3751
pseudospectral methoderror estimatenonlinear Klein-Gordon equationlow regularityexponential-type integratortime symmetric
Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geometric numerical integration and Schrödinger equations
- Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
- The global Cauchy problem for the nonlinear Klein-Gordon equation
- The global Cauchy problem for the nonlinear Klein-Gordon equation. II
- Numerical solution of a nonlinear Klein-Gordon equation
- A study of extrapolation methods based on multistep schemes without parasitic solutions
- Fourier collocation method for solving nonlinear Klein-Gordon equation
- Modulated Fourier expansions of highly oscillatory differential equations
- Low regularity exponential-type integrators for semilinear Schrödinger equations
- Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations
- On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
- A Gautschi-type method for oscillatory second-order differential equations
- Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
- A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
- Embedded exponential-type low-regularity integrators for KdV equation under rough data
- Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
- A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
- Two exponential-type integrators for the ``good Boussinesq equation
- An exponential-type integrator for the KdV equation
- Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
- Numerical integration of ordinary differential equations based on trigonometric polynomials
- A note on the Gautschi-type method for oscillatory second-order differential equations
- Exponential integrators
- Spectral Methods
- Geometric Numerical Integration
- Product Approximation for Nonlinear Klein-Gordon Equations
- Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
- Spectral Methods in MATLAB
- Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
- Accelerating the Nonuniform Fast Fourier Transform
- Nonexistence of global solutions of the initial-boundary value problem for the nonlinear Klein–Gordon equation
- A General Framework of Low Regularity Integrators
- Resonance-based schemes for dispersive equations via decorated trees
- A first-order Fourier integrator for the nonlinear Schrödinger equation on 𝕋 without loss of regularity
- Uniformly Accurate Low Regularity Integrators for the Klein--Gordon Equation from the Classical to NonRelativistic Limit Regime
- Low-regularity integrators for nonlinear Dirac equations
- A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime
- A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data
- On Time-Splitting Pseudospectral Discretization for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime
- Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
- An Exponential Wave Integrator Sine Pseudospectral Method for the Klein--Gordon--Zakharov System