Global error bounds of one-stage extended RKN integrators for semilinear wave equations (Q2316632)

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English	Global error bounds of one-stage extended RKN integrators for semilinear wave equations	scientific article

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title

Global error bounds of one-stage extended RKN integrators for semilinear wave equations (English)

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6 August 2019

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full work available at URL

https://arxiv.org/abs/1801.02070

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zbMATH Keywords

error bounds

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semilinear wave equations

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extended Runge-Kutta-Nyström integrators

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trigonometric integrators

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LIMbook

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MaRDI publication profile

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cites work

Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime

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Energy conservation issues in the numerical solution of the semilinear wave equation

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Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

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Stability and convergence of trigonometric integrator pseudospectral discretization for \textit{N}-coupled nonlinear Klein-Gordon equations

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Geometric numerical integration and Schrödinger equations

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Long-Time-Step Methods for Oscillatory Differential Equations

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Error Analysis of Trigonometric Integrators for Semilinear Wave Equations

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Convergence of a split-step Hermite method for the Gross-Pitaevskii equation

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Trigonometric integrators for quasilinear wave equations

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Metastable energy strata in numerical discretizations of weakly nonlinear wave equations

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On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations

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Q5292004

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Error analysis of exponential integrators for oscillatory second-order differential equations

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Spectral semi-discretisations of weakly non-linear wave equations over long times

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Geometric Numerical Integration

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A Gautschi-type method for oscillatory second-order differential equations

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Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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Exponential Rosenbrock-Type Methods

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Exponential integrators

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Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations

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Operator splitting for partial differential equations with Burgers nonlinearity

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On the global error of discretization methods for highly-oscillatory ordinary differential equations

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Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics

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Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type

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Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems

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Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

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Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

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On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

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An Essential Extension of the Finite-Energy Condition for Extended Runge-Kutta-Nyström Integrators when Applied to Nonlinear Wave Equations

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Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations

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Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

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Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations

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ERKN integrators for systems of oscillatory second-order differential equations

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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

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Identifiers

zbMATH Open document ID

1422.65229

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DOI

10.1007/s11075-018-0585-0

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Mathematics Subject Classification ID

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Mathematics(1 entry)

mardi Publication:2316632