Error Analysis of Trigonometric Integrators for Semilinear Wave Equations

DOI10.1137/140977217zbMath1457.65076arXiv1407.3042OpenAlexW2963015717MaRDI QIDQ5253602

Ludwig J. Gauckler

Publication date: 27 May 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.3042

zbMATH Keywords

semilinear wave equationerror boundsnonlinear wave equationStörmer-Verlet methodexponential integratorsleapfrog methodtrigonometric integrators

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Error bounds for numerical methods for ordinary differential equations (65L70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (22)

Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation ⋮ On a splitting method for the Zakharov system ⋮ Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations ⋮ Trigonometric integrators for quasilinear wave equations ⋮ Asymptotic preserving trigonometric integrators for the quantum Zakharov system ⋮ Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data ⋮ A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation ⋮ One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations ⋮ Numerical conservations of energy, momentum and actions in the full discretisation for nonlinear wave equations ⋮ Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting ⋮ Semi-analytical exponential RKN integrators for efficiently solving high-dimensional nonlinear wave equations based on FFT techniques ⋮ Uniformly Accurate Oscillatory Integrators for the Klein--Gordon--Zakharov System from Low- to High-Plasma Frequency Regimes ⋮ Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation ⋮ Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations ⋮ Metastable energy strata in numerical discretizations of weakly nonlinear wave equations ⋮ On averaged exponential integrators for semilinear wave equations with solutions of low-regularity ⋮ Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi-linear highly oscillatory hyperbolic systems ⋮ A modified Gautschi's method without order reduction when integrating boundary value nonlinear wave problems ⋮ Long-time momentum and actions behaviour of energy-preserving methods for semi-linear wave equations via spatial spectral semi-discretisations ⋮ Global error bounds of one-stage extended RKN integrators for semilinear wave equations ⋮ Error Analysis of Trigonometric Integrators for Semilinear Wave Equations ⋮ On nested Picard iterative integrators for highly oscillatory second-order differential equations

Cites Work

• Unnamed Item
• Geometric numerical integration and Schrödinger equations
• Spectral semi-discretisations of weakly non-linear wave equations over long times
• Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
• A study of extrapolation methods based on multistep schemes without parasitic solutions
• Stability and convergence of trigonometric integrator pseudospectral discretization for \textit{N}-coupled nonlinear Klein-Gordon equations
• A Gautschi-type method for oscillatory second-order differential equations
• Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
• High-order symmetric multistep cosine methods
• Conservation of invariants by symmetric multistep cosine methods for second-order partial differential 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
• Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics
• Convergence of a split-step Hermite method for the Gross-Pitaevskii equation
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Multistep cosine methods for second-order partial differential systems
• Long-Time-Step Methods for Oscillatory Differential Equations
• Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
• Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
• Operator splitting for partial differential equations with Burgers nonlinearity
• A Trigonometric Method for the Linear Stochastic Wave Equation
• Error Analysis of Trigonometric Integrators for Semilinear Wave Equations
• Error analysis of exponential integrators for oscillatory second-order differential equations
• Geometric Numerical Integration

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