Spectral Jacobi approximations for Boussinesq systems

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Cites Work

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Wave breaking in Boussinesq models for undular bores
On high order strong stability preserving Runge-Kutta and multi step time discretizations
High order strong stability preserving time discretizations
Strong stability of singly-diagonally-implicit Runge-Kutta methods
Numerical solution of Boussinesq systems of the Bona-Smith family
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Legendre and Chebyshev spectral approximations of Burgers' equation
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Exact traveling-wave solutions to bidirectional wave equations
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SDIRK methods for stiff ODEs with oscillating solutions
Exact solutions of various Boussinesq systems
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A Boussinesq system for two-way propagation of nonlinear dispersive waves
Construction of SDIRK methods with dispersive stability functions
Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models
A numerical study of the stability of solitary waves of the Bona-Smith family of Boussinesq systems
Strong stability-preserving high-order time discretization methods
Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking
Spectral Methods
Approximation Results for Orthogonal Polynomials in Sobolev Spaces
Phase-Lag Analysis of Implicit Runge–Kutta Methods
Properties of Some Weighted Sobolev Spaces and Application to Spectral Approximations
A Finite Element Method for a Version of the Boussinesq Equation
A model for the two-way propagation of water waves in a channel
Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

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