Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter

DOI10.1007/s10543-022-00925-zzbMath1502.65158arXiv2105.03732OpenAlexW3162776474MaRDI QIDQ2100552

María Cabrera Calvo, Katharina Schratz

Publication date: 22 November 2022

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.03732

zbMATH Keywords

convergencenumerical schemeBenjamin-Bona-Mahony equation

Mathematics Subject Classification ID

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) Numerical methods for initial value problems involving ordinary differential equations (65L05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Cites Work

• Strang splitting method to Benjamin-Bona-Mahony type equations: analysis and application
• An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime
• On the global attractor for the damped Benjamin-Bona-Mahony equation
• Splitting methods with complex times for parabolic equations
• High order splitting methods for analytic semigroups exist
• Splitting methods for the time-dependent Schrödinger equation
• Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation
• On the necessity of negative coefficients for operator splitting schemes of order higher than two
• Composition methods in the presence of small parameters
• Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
• Convergence error estimates at low regularity for time discretizations of KdV
• Approximate model equations for water waves
• Operator splitting for the KdV equation
• Splitting methods
• A high-order Petrov-Galerkin finite element method for the classical Boussinesq wave model
• Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions
• The generalized Benjamin-Bona-Mahony equation in n with singular initial data
• Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
• Operator splitting for partial differential equations with Burgers nonlinearity
• A General Framework of Low Regularity Integrators
• Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity
• Finite volume methods for unidirectional dispersive wave models
• Geometric Numerical Integration

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