Two energy-preserving compact finite difference schemes for the nonlinear fourth-order wave equation

DOI10.1007/S42967-022-00193-2OpenAlexW4281929653MaRDI QIDQ2084927

Qiaoqiao Xu, Shilong Jin, Xiaoyi Liu, Ting-chun Wang

Publication date: 13 October 2022

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-022-00193-2

zbMATH Keywords

iterative algorithmerror estimateenergy conservationcompact finite difference schemenonlinear fourth-order wave equation

Mathematics Subject Classification ID

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Cites Work

• Unnamed Item
• Unnamed Item
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• A three level linearized compact difference scheme for the Cahn-Hilliard equation
• Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term
• On the initial value problem of the semilinear beam equation with weak damping. II: Asymptotic profiles
• High-fidelity numerical simulation of the dynamic beam equation
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Existence and uniqueness results for the bending of an elastic beam equation at resonance
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
• Decay estimates for fourth order wave equations
• Stability and instability of fourth-order solitary waves
• Time decay for the nonlinear beam equation
• Long-time existence for semi-linear beam equations on irrational tori
• Conservative finite difference scheme for the nonlinear fourth-order wave equation
• An exact solution for variable coefficient fourth-order wave equation using the Adomian method
• Scattering and the Levandosky-Strauss conjecture for fourth-order nonlinear wave equations
• Local time decay for a nonlinear beam equation
• Finite difference discretization of the cubic Schrödinger equation
• Simulation of Wave Interactions and Turbulence in One-Dimensional Water Waves
• Discrete-Time Orthogonal Spline Collocation Methods for Vibration Problems
• Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime
• 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
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES
• Spatial patterns. Higher order models in physics and mechanics

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