A numerical solution to Klein-Gordon equation with Dirichlet boundary condition

DOI10.1016/j.amc.2003.11.014zbMath1126.65090OpenAlexW2116967396MaRDI QIDQ706774

Mahmoud Elgamal, M. E. Khalifa

Publication date: 9 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.11.014

zbMATH Keywords

algorithmfinite element methodnumerical examplesRunge-Kutta methodexistence and uniquenessGauss-Legendre quadratureKlein-Gordon wave equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Optimal control of damped Klein-Gordon equations with state constraints, Conservative difference methods for the Klein-Gordon-Zakharov equations, Numerical solution of the Klein-Gordon equation via He's variational iteration method, Uniformly accurate nested Picard iterative integrators for the Klein-Gordon equation in the nonrelativistic regime, Global existence and uniform decay of a damped Klein-Gordon equation in a noncylindrical domain, The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation, On the solution behavior of a nonlinear time-fractional Klein-Gordon equation: theoretical study and numerical validation, A numerical scheme based on differential quadrature method for numerical simulation of nonlinear Klein-Gordon equation, Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime, A new method to solve the damped nonlinear Klein-Gordon equation, Numerical simulation for the initial-boundary value problem of the Klein-Gordon-Zakharov equations, Collocation and finite difference-collocation methods for the solution of nonlinear Klein-Gordon equation, Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation, An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain, A class of nonlinear parabolic-hyperbolic equations applied to image restoration

Uses Software

• dverk

Cites Work

• Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system
• Infinite-dimensional dynamical systems in mechanics and physics
• Weak solutions to quasilinear wave equations of Klein-Gordon or sine-Gordon type and relaxation to reaction-diffusion equations
• Equivalent Norms for Sobolev Spaces
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