Fetching the paper…
Reading the bibliography…
We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations.
W. Gautschi, Construction of Gauss–Christoffel quadrature formulas, Math. Comput. 22 (1968) 251–270
1968
Earlier work this paper cites.
B. Shizgal, A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems, Journal of Computational Physics 41 (1981) 309–328
1981
Earlier work this paper cites.
W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Stat. Comput. 3 (3) (1982) 289–317
1982
Earlier work this paper cites.
E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, Krieger Publishing Company, Malabar, Florida, 1984
1984
Earlier work this paper cites.
R. Hazeltine, J. Meiss, Plasma Confinement, Frontiers in Physics, Addison-Wesley, Redwood City, 1992
1992
Earlier work this paper cites.
M. Hajmirzaahmad, A. M. Krall, Singular second-order operators: The maximal and minimal operators, and selfadjoint operators in between, SIAM Review 34 (4) (1992) 614–634
1992
Earlier work this paper cites.
M. Kotschenreuther, G. Rewoldt, W.M. Tang, Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities, Comput. Phys. Commun. 88 (1995) 128-140
1995
Earlier work this paper cites.
J. W. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997
1997
Earlier work this paper cites.
R. Hazeltine, F. Waelbroeck, The Framework of Plasma Physics, Perseus, Reading,MA, 1998
1998
Earlier work this paper cites.
I. Stakgold, Green’s functions and boundary value problems, Wiley, New York, 1998
1998
Earlier work this paper cites.
A. J. Cox, N. J. Higham, Stability of Householder QR factorization for weighted least squares problems, in: Proceedings of the 17th Dundee Biennial Conference, Vol. 380 of Pitman Research Notes in Mathematics, Addison Wesley Longman, Harlow, Essex, UK, 1998, pp. 57–73
1998
Earlier work this paper cites.
E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I
2000
Cited alongside, same era.
P. Helander, D. Sigmar, Collisional Transport in Magnetized Plasmas, Cambridge University Press, Cambridge, 2002
2002
Cited alongside, same era.
J.S. Ball, Half-range generalized Hermite polynomials and the related Gaussian quadratures, SIAM J. Numer. Anal. 40 (2003) 2311-2317
2003
Cited alongside, same era.
C. A. Kennedy, M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math. 44 (1–2) (2003) 139–181
2003
Cited alongside, same era.
J. Candy and R.E. Waltz, An Eulerian gyrokinetic-Maxwell solver, J. Comp. Phys. 186 (2003) 545-581
2003
Cited alongside, same era.
J. Candy, C. Holland, R. Waltz, M. Fahey, E. Belli, Tokamak profile prediction using direct gyrokinetic and neoclassical simulation, Physics of Plasmas 16 (2009) 060704
2009
Later among the works it cites.
M. Barnes, I. Abel, W. Dorland, D. Ernst, G. Hammett, P. Ricci, B. Rogers, A. Schekochihin, T. Tatsuno, Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests, Physics of Plasmas 16 (2009) 072107
2009
Later among the works it cites.
M. Barnes, I. Abel, W. Dorland, T. Görler, G. Hammett, F. Jenko, Direct multiscale coupling of a transport code to gyrokinetic turbulence codes, Physics of Plasmas 17 (2010) 056109
2010
Later among the works it cites.
M. Barnes, W. Dorland, and T. Tatsuno, Resolving velocity space dynamics in continuum gyrokinetics, Phys. Plasmas 17 (2010), 032106
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A.-K. Kassam, L. N. Trefethen, Fourth-order time-stepping for stiff PDEs, SIAM J. Sci. Comput. 26 (4) (2005) 1214–1233
2005
Cited alongside, same era.
J. Wilkening, An algorithm for computing Jordan chains and inverting analytic matrix functions, Linear Algebra Appl. 427 (2007) 6–25
2007
Cited alongside, same era.
A. A. Schekochihin, S. C. Cowley, W. Dorland, G. W. Hammett, G. G. Howes, G. G. Plunk, E. Quataert, T. Tatsuno. Gyrokinetic turbulence: a nonlinear route to dissipation through phase space, Plasma Physics and Controlled Fusion 50 (2008) 124024
2008
Cited alongside, same era.
I. Abel, M. Barnes, S. Cowley, W. Dorland, A. Schekochihin, Linearized model Fokker–Planck collision operators for gyrokinetic simulations. I. Theory, Physics of Plasmas 15 (2008) 122509
2008
Cited alongside, same era.
C. Fulton, Titchmarsh–Weyl m m -functions for second-order Sturm–Liouville problems with two singular endpoints, Math. Nachr. 281 (10) (2008) 1418–1475
2008
Cited alongside, same era.
J. Wilkening, A. Cerfon, M. Landreman, Symmetric pseudo-spectral velocity discretization schemes for kinetic equations with energy diffusion (in preparation)
Cited in the paper.
R. Numata, G.G. Howes, T. Tatsuno, M. Barnes, W. Dorland, AstroGK: Astrophysical gyrokinetics code, J. Comp. Phys. 229 (2010) 9347–9372
2010
Later among the works it cites.
D. R. Hatch, P. W. Terry, F. Jenko, F. Merz, W. M. Nevins, Saturation of gyrokinetic turbulence through damped eigenmodes, Phys. Rev. Lett. 106 (2011) 115003
2011
Later among the works it cites.
V. Bratanov, F. Jenko, D. Hatch, S. Brunner, Aspects of linear Landau damping in discretized systems, Physics of Plasmas 20 (2013) 022108
2013
Later among the works it cites.
M. Landreman, D. Ernst, New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions, Journal of Computational Physics 243 (2013) 130–150
2013
Later among the works it cites.
G.P. Ghiroldi, L. Gibelli, A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization, J. Comp. Phys. 258 (2014) 568 - 584
2014
Closest in time.
J. Wilkening, A. Cerfon, A Spectral Transform Method for Singular Sturm–Liouville Problems with Applications to Energy Diffusion in Plasma Physics, SIAM J. Appl. Math., (accepted), 2015
2015
Closest in time.