The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions

DOI10.1016/j.apnum.2019.12.024zbMath1434.65111OpenAlexW2999454470WikidataQ126403269 ScholiaQ126403269MaRDI QIDQ2301391

Dingwen Deng, Dong Liang

Publication date: 24 February 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.12.024

zbMATH Keywords

convergencesolvabilityenergy conservationenergy preserving FDMsnonlinear wave equation system

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Second-order nonlinear hyperbolic equations (35L70) 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)

Related Items (15)

Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations ⋮ The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations ⋮ Efficient high-order physical property-preserving difference methods for nonlinear fourth-order wave equation with damping ⋮ Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping ⋮ Energy-preserving finite element methods for a class of nonlinear wave equations ⋮ Energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon equation and coupled sine-Gordon equations ⋮ Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations ⋮ Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system ⋮ Unnamed Item ⋮ Error estimations of the fourth-order explicit Richardson extrapolation method for two-dimensional nonlinear coupled wave equations ⋮ Accuracy improvement of a predictor-corrector compact difference scheme for the system of two-dimensional coupled nonlinear wave equations ⋮ An energy-conserving finite element method for nonlinear fourth-order wave equations ⋮ High-order structure-preserving Du Fort-Frankel schemes and their analyses for the nonlinear Schrödinger equation with wave operator ⋮ A class of weighted energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon-type equations ⋮ The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations

Uses Software

• Matlab
• LIMbook

Cites Work

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• Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations
• Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
• Exact solutions of coupled sine-Gordon equations
• Numerical solution of a nonlinear Klein-Gordon equation
• Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation
• The use of radial basis functions (RBFs) collocation and RBF-QR methods for solving the coupled nonlinear sine-Gordon equations
• Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations
• The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations
• Global solutions and finite time blow up for some system of nonlinear wave equations
• The periodic solutions for a class of coupled nonlinear Klein-Gordon equations
• On the exchange of energy in coupled Klein --- Gordon equations
• Compactons, solitons and periodic solutions for some forms of nonlinear Klein--Gordon equations
• The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations
• Line Integral Methods for Conservative Problems
• Convergence of a Second-Order Scheme for Semilinear Hyperbolic Equations in 2 + 1 Dimensions
• Asymptotic behavior of the solutions of a nonlinear system of Klein-Gordon equations
• Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
• Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection

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