Ph.D. Thesis: The Effect of Upper Level Features in The Atmosphere on Linear Theory and Linearized BenjaminDavisOno Theory for Internal Gravity Waves, University of Michigan Press, Ann Arbor, 1999.

N. Flyer, Asymptotic upper bounds for the coefficients in the Chebyshev series expansion for a
general order integral of a function, Mathematics of Computation, 67, 16011616, 1998.

K. Kabin and N. Flyer, Reminiscences about difference schemes by Sergei Konstantinovich Godunov (translation from Russian), Journal of Computational Physics, 153, 625, 1999.

J. P. Boyd and N. Flyer, Compatibility conditions for timedependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods, Computer Methods in Applied Mechanics and Engineering, 175, 281309, 1999.

N. Flyer and P. N. Swarztrauber, Convergence of spectral and finite difference methods for initial boundary value problems, SIAM J. of Scientific Computing, 23(5), 17311751, 2002.

N. Flyer and B. Fornberg, Accurate numerical solution of initial transients in convectivediffusive equations, Journal of Computational Physics, 184(2), 526539, 2003.

N. Flyer and B. Fornberg, On the nature of initialboundary value solutions for dispersive equations, SIAM Journal of Applied Mathematics, 64(2), 546564, 2004.

N. Flyer, B. Fornberg, S. Thomas and B.C. Low, Magnetic field confinement in the solar corona. I. Forcefree fields, The Astrophysical Journal, 606, 12101222, 2004.

N. Flyer, B. Fornberg, S. Thomas and B.C. Low, Magnetic field confinement in the solar corona. II. The weight of plasmas, The Astrophysical Journal, 631, 12391259, 2005.

B. Fornberg and N. Flyer, Accuracy of radial basis function interpolation and derivative approximations in 1D, Advances in Computational Mathematics, 23, 520, 2005.

M. Zhang, N. Flyer, B.C. Low, Magnetic field confinement in the corona: The role of magnetic
helicity accumulation, The Astrophysical Journal, 644(1), 575586, 2006.

N. Flyer, Exact polynomial reproduction for oscillatory radial basis functions on infinite lattices,
Computers and Mathematics with Applications, 51(8), 11991208, 2006.

N. Flyer and G.B. Wright, Transport schemes on a sphere using radial basis functions, J. Comput. Phys., 226, 10591084, 2007.

B.C. Low and N. Flyer, The topological nature of boundary value problems for forcefree magnetic field, The Astrophysical Journal, 668(1), 557570, 2007.

B. Fornberg, N. Flyer, S. Hovde, C. Piret, Locality properties of radial basis function expansion
coefficients for equispaced interpolation, IMA J. of Numerical Analysis, 28, 121142, 2008.

A. Malmberg, A. Arellano, D. P Edwards, N. Flyer, D. Nychka, and C. K Wikle, Interpolating fields of carbon monoxide data using a hybrid statisticalphysical Model, Annals of Applied Statistics, 2(4), 12311248, 2008.

N. Flyer and A.S. Fokas, A new method for the numerical integration of evolutionary partial
differential equations. I. The half line, Proc. Roy. Soc. A, 464(2095), 18231849, 2008.

M. Zhang and N. Flyer, The dependence of the helicity bound of forcefree magnetic fields on
boundary conditions, The Astrophysical Journal, 683(2), 1160–1167, 2008.

N. Flyer and G.B. Wright, A radial basis function method for the shallow water equations on a sphere, Proceedings of the Royal Society A, 465, 19491976, 2009.

A.S. Fokas, N. Flyer, S.A. Smitherman, E. Spence, A semianalytical numerical method for solving evolution and elliptic partial differential equations, J. Comput. Appl. Math., 227, 5974, 2009.

K. Miller, B. Fornberg, N. Flyer, and B.C. Low, Magnetic relaxation of the solar corona, The
Astrophysical Journal, 690, 720733, 2009.

B. Fornberg, N. Flyer, and J.M. Russell, Comparisons between pseudospectral and radial basis
function derivative approximations, IMA Journal of Numerical Analysis, 30, 149172, 2010.

N. Flyer and E. Lehto, Rotational transport on a sphere: Local node refinement with radial basis functions, J. Comput. Phys., 229, 19541969, 2010.

G.B. Wright, N. Flyer and D.A. Yuen, A hybrid radial basis function pseudospectral method for thermal convection in a 3D spherical shell, Geophys., Geochem., Geosyst., 11, Q07003, 2010.

N. Flyer and B. Fornberg, Radial basis functions: Developments and applications to planetary scale flows, Computers and Fluids, 46, 2332, 2011.

B. Fornberg, E. Larsson, and N. Flyer, Stable computations with Gaussian radial functions, SIAM J. Sci. Comput., 33(2), 869892, 2011.

Fornberg, B. and Flyer N., Some numerical tests on Laplace’s equation with the Fokas boundary integral approach, Proc Roy. Soc. A, 467(2134), 29833003, 2011.

N. Flyer, Z. Qin, and R. Temam, A penalty method for numerically handling dispersive equations with incompatible initial and boundary data, Num. Meth. PDEs, 28(6), 19962009, 2012.

N. Flyer, E. Lehto, S. Blaise, G. Wright, A. and St. Cyr, RBFgenerated finite differences for nonlinear transport on a sphere: shallow water simulations, J. Comput. Phys., 231(11), 40784095, 2012.
 M. Zhang, N. Flyer, and B.C. Low, Magnetic helicity of selfsimilar axisymmetric forcefree fields, ApJ, 755(1), 78, 2012.

E. Bollig, N. Flyer, and G. Erlebacher,Using radial basis function finite difference (RBFFD) for PDE Solutions on the GPU, J. Comput. Phys., 231(21), 7133–7151, 2012.
 G. Erlebacher, E. Saule, N. Flyer, E. Bollig , Acceleration of Derivative Calculations with Application to Radial Basis Function – FiniteDifferences on the Intel MIC Architecture, Proceedings of the International Conference on Supercomputing (referred  15% acceptance rate with 25 out of 167 submissions accepted), June 2014.

M. Tillenius, E. Larsson, E. Lehto and N. Flyer, A task parallel implementation of a scattered node stencilbased solver for the shallow water equations, MCC2013  Sixth Swedish Workshop on Multicore Computing, (referred proceeding), November 2013.
 P.A. Arrial, N. Flyer, G. B. Wright, L.H. Kellogg, On the sensitivity of 3D thermal convection codes to numerical discretization: A model intercomparison, Geosci. Model Dev., 7, 20652076, 2014.

B. Fornberg and N. Flyer, Fast generation of 2D node distributions for meshfree PDE discretizations, Comput. Math Appli., 69 (7), 531544, 2015.

M Tillenius, E Larsson, E Lehto, N Flyer, A scalable RBF–FD method for atmospheric flow, J. Comput. Phys. 298, 406422, 2015.