One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations

DOI10.1007/s10092-023-00506-8OpenAlexW2969704601MaRDI QIDQ2685995

Bin Wang, Ting Li, Chang Ying Liu

Publication date: 23 February 2023

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.02252

zbMATH Keywords

second-order convergencetrigonometric integratorsquasilinear wave equationsenergy technique

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Cites Work

• Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations
• ERKN integrators for systems of oscillatory second-order differential equations
• Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type
• Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
• Partial differential equations. III: Nonlinear equations.
• Pseudodifferential operators and nonlinear PDE
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Lectures on nonlinear hyperbolic differential equations
• Stability and convergence of trigonometric integrator pseudospectral discretization for \textit{N}-coupled nonlinear Klein-Gordon equations
• Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations
• Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations
• Global and almost global existence for general quasilinear wave equations in two space dimensions
• Conservation of invariants by symmetric multistep cosine methods for second-order partial differential equations
• A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations
• Well-posedness of solutions for a class of quasilinear wave equations with structural damping or strong damping
• Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
• Numerical approximation and simulation of the stochastic wave equation on the sphere
• On one-dimension quasilinear wave equations with null conditions
• Solving the wave equation with multifrequency oscillations
• A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein-Gordon equations
• Global error bounds of one-stage extended RKN integrators for semilinear wave equations
• Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations
• Justification of the nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation
• Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations
• Modulating pulse solutions for quasilinear wave equations
• Structure-Preserving Algorithms for Oscillatory Differential Equations II
• Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part II: Convergence
• Local well-posedness of a quasilinear wave equation
• Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity
• Exponential integrators
• Trigonometric integrators for quasilinear wave equations
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Structure-Preserving Algorithms for Oscillatory Differential Equations
• A Trigonometric Method for the Linear Stochastic Wave Equation
• NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms
• The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations
• Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part I: Stability
• Error Analysis of Trigonometric Integrators for Semilinear Wave Equations
• Geometric Numerical Integration
• Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
• A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators

This page was built for publication: One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations