Conservative finite difference scheme for the nonlinear fourth-order wave equation
From MaRDI portal
Publication:2279410
DOI10.1016/j.amc.2019.04.033zbMath1429.65177OpenAlexW2943916837WikidataQ127940450 ScholiaQ127940450MaRDI QIDQ2279410
Publication date: 12 December 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2019.04.033
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order semilinear hyperbolic equations (35L76)
Related Items (13)
An efficient tool for solving the Rosenau-Burgers equation in two dimensions ⋮ Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions ⋮ Efficient high-order physical property-preserving difference methods for nonlinear fourth-order wave equation with damping ⋮ High-order compact difference methods for solving two-dimensional nonlinear wave equations ⋮ Efficient and accurate numerical methods for nonlinear strongly damped wave equation in 2+1 dimensions ⋮ Higher-order energy-preserving difference scheme for the fourth-order nonlinear strain wave equation ⋮ A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations ⋮ Analysis of finite difference schemes for a fourth-order strongly damped nonlinear wave equations ⋮ Two conservative and linearly-implicit compact difference schemes for the nonlinear fourth-order wave equation ⋮ On the \(L^{\infty}\)-convergence of two conservative finite difference schemes for fourth-order nonlinear strain wave equations ⋮ A family of effective structure-preserving schemes with second-order accuracy for the undamped sine-Gordon equation ⋮ Two energy-preserving compact finite difference schemes for the nonlinear fourth-order wave equation ⋮ An energy-conserving finite element method for nonlinear fourth-order wave equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term
- On the \(L_\infty \) convergence of a difference scheme for coupled nonlinear Schrödinger equations
- On symplectic and multisymplectic schemes for the KdV equation
- Energy conservation issues in the numerical solution of the semilinear wave equation
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- Nonlinear oscillations in a suspension bridge
- Global existence and exponential stability of small solutions to nonlinear viscoelasticity
- Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
- Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
- Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
- Decay estimates for fourth order wave equations
- Stability and instability of fourth-order solitary waves
- Time decay for the nonlinear beam equation
- Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
- Scattering and the Levandosky-Strauss conjecture for fourth-order nonlinear wave equations
- Local time decay for a nonlinear beam equation
- Line Integral Methods for Conservative Problems
- A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- Simulating Hamiltonian Dynamics
- Travelling Waves in a Suspension Bridge
- Local Smoothing Properties of Dispersive Equations
- On the quasilinear wave equation: utt − Δu + f(u, ut) = 0 associated with a mixed nonhomogeneous condition
- Geometric integration using discrete gradients
- Simulation of Wave Interactions and Turbulence in One-Dimensional Water Waves
- Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
- Nonlinear Wave Interactions in Nonlinear Nonintegrable Systems
- Stepwise Precession of the Resonant Swinging Spring
- Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
- Spatial patterns. Higher order models in physics and mechanics
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
- Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
This page was built for publication: Conservative finite difference scheme for the nonlinear fourth-order wave equation
