A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein-Gordon equations

DOI10.1016/j.apnum.2019.02.009zbMath1439.35417OpenAlexW2919152404MaRDI QIDQ2311786

Bin Wang, Xin-Yuan Wu

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.02.009

zbMATH Keywords

convergencenonlinear stabilityoperator-variation-of-constants formulasemi-linear Klein-Gordon equationssymplectic approximations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation ⋮ Exponential basis and exponential expanding grids third (fourth)-order compact schemes for nonlinear three-dimensional convection-diffusion-reaction equation ⋮ One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations ⋮ Two conservative and linearly-implicit compact difference schemes for the nonlinear fourth-order wave equation ⋮ An approach to solving Maxwell's equations in time domain

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