The symbol approximation method: a numerical approach to the approximation of the symbol of self-adjoint operators

Abdelouhab L, Bona JL, Fellant M, Saut J-C (1989) Nonlocal models for nonlinear dispersive waves. Phys D 40:360–392

Avron H, Toledo S (2011) Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix. JACM 58:1–34

Bai Z, Fahey G, Golub G (1996) Some large-scale matrix computation problems. J Comput Appl Math 74(1):71–89

Bona JL, Kalisch H (2004) Singularity formation in the generalized Benjamin-Ono equations. Discrete Contin Dyn Syst 11(1):27–45

Brezinski C (2000) Convergence acceleration during the 20th century. J Comput Appl Math 122:1–21. Numerical Analysis in the 20th Century Vol. II: Interpolation and Extrapolation

Brezinski C, Redivo-Zaglia M (1991) Extrapolation methods. Theory and practice. North-Holland, Amsterdam

Brooke Benjamin T (1967) Internal waves of permanent form in fluids of great depth. J Fluid Mech 29(3):559

Cabral M, Rosa R (2004) Chaos for a damped and forced KdV equation. Phys D 192:265–278

Cahouet J, Chabard J-P (1988) Some fast 3d finite element solvers for the generalized Stokes problem. Int J Numer Methods Fluids 8:869–895

Chehab J-P (1998) Incremental unknowns method and compact schemes. ESAIM Math Model Numer Anal 32(1):51–83

Chehab J-P (2021) Stabilization and numerical filtering for the modeling and the simulation of time dependent PDEs. Discrete Contin Dyn Syst 14(8):2693–2728

Chehab J-P, Sadaka G (2013a) Numerical Study of a family of dissipative KdV equations. Commun Pure Appl Anal 12:519–546

Chehab J-P, Sadaka G (2013b) On Damping Rates of dissipative KdV equations. Discrete Contin Dyn Syst Ser S 6:1487–1506

Chehab JP, Garnier P, Mammeri Y (2015) Long-time behavior of solutions of a BBM equation with generalized damping. Discrete Contin Dyn Syst B, 1897–1915

Chen M, Dumont S, Dupaigne L, Goubet O (2010) Decay of solutions to a water wave model with nonlocal viscous dispersive term. Discrete Contin Dyn Syst 27:1473–1492

Dias F, Dutykh D (2007) Viscous potential free-surface flows in a fluid layer of finite depth. C R Math Acad Sci Paris 345:113–118

Dumont S, Manoubi I (2018) Numerical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach. Math Methods Appl Sci 41(12):4810–4826

Dutykh D (2009) Viscous-potential free-surface flows and long wave modeling. Eur J Mech B Fluids 28:430

Dutykh D, Le Meur HVJ (2021) Derivation of a viscous Serre–Green–Naghdi equation: an impasse? Fluids 6(4):135

Goubet O, Zahrouni E (2008) On time discretization of a weakly damped forced nonlinear Schrödinger equation. Commun Pure Appl Anal 7(6):1429–1442

Hedayat AS, Wallis WD (1978) Hadamard matrices and their applications. Ann Stat 6(6):1184–1238

Hutchinson MF (1989) A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Commun Stat Simul Comput 18:1059–1076

Jäger D (1982) Experiments on KdV solitons. J Phys Soc Jpn 51:1686–1693

Kuttler JR, Sigillito VG (1984) Eigenvalues of the Laplacian in two dimensions. SIAM Rev 26(2):163–193

Le Meur HVJ (2015) Derivation of a viscous Boussinesq system for surface water waves. Asymptot Anal 94(3–4):30–345

Lele S (1992) Compact difference schemes with spectral like resolution. J Comput Phys 103:16–42

Ono H (1975) Algebraic solitary waves in stratified fluids. J Phys Soc Jpn 39(4):1082–1091

Ott E, Sudan RN (1969) Nonlinear theory of ion acoustic wave with Landau damping. Phys Fluids 12:2388–2394

Ott E, Sudan RN (1970) Damping of solitary waves. Phys Fluids 13:1432–1435

Peyret R, Taylor R (1983) Computational methods for fluid flow, Springer Series in Computational Physics. Springer, New York

Ubaru S, Saad Y (2018) Applications of trace estimation techniques. In: High performance computing in science and engineering, pp 19–33