Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations
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Publication:1986166
DOI10.1016/j.apnum.2020.02.020zbMath1436.65197OpenAlexW3012067494MaRDI QIDQ1986166
Publication date: 7 April 2020
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2020.02.020
nonlinear stabilitysemi-linear wave equationFourier spectral methodsglobal error analysisenergy techniquesERKN integratornonlinear multi-frequency highly oscillatory system
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) 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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Related Items (7)
Optimized pairs of multidimensional ERKN methods with FSAL property for multi-frequency oscillatory systems ⋮ A novel class of explicit two-step Birkhoff-Hermite integrators for highly oscillatory second-order differential equations ⋮ A fourth-order energy-preserving and symmetric average vector field integrator with low regularity assumption ⋮ High-order symmetric and energy-preserving collocation integrators for the second-order Hamiltonian system ⋮ Explicit pseudo two-step exponential Runge-Kutta methods for the numerical integration of first-order differential equations ⋮ An integral evolution formula of boundary value problem for wave equations ⋮ Two high-order energy-preserving and symmetric Gauss collocation integrators for solving the hyperbolic Hamiltonian systems
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