[1] Boyd, J. P.:
Chebyshev and Fourier Spectral Methods. Dover Publications, Mineola (2001).
MR 1874071 |
Zbl 0994.65128
[2] Brigham, E.: Fast Fourier Transform and Its Applications. Prentice Hall, Upper Saddle River (1988).
[4] Day, S., Hiraoka, Y., Mischaikow, K., Ogawa, T.:
Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. SIAM J. Appl. Dyn. Syst. 4 (2005), 1-31.
DOI 10.1137/040604479 |
MR 2136516 |
Zbl 1058.35050
[5] Day, S., Junge, O., Mischaikow, K.:
A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. SIAM J. Appl. Dyn. Syst. 3 (2004), 117-160.
DOI 10.1137/030600210 |
MR 2067140 |
Zbl 1059.37068
[6] Day, S., Kalies, W. D.:
Rigorous computation of the global dynamics of integrodifference equations with smooth nonlinearities. SIAM J. Numer. Anal. 51 (2013), 2957-2983.
DOI 10.1137/120903129 |
MR 3124898 |
Zbl 1288.37030
[8] Figueras, J.-L., Llave, R. de la:
Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. SIAM J. Appl. Dyn. Syst. 16 (2017), 834-852.
DOI 10.1137/16M1073790 |
MR 3633778 |
Zbl 1370.65047
[15] Hungria, A., Lessard, J.-P., James, J. D. Mireles:
Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach. Math. Comput. 85 (2016), 1427-1459.
DOI 10.1090/mcom/3046 |
MR 3454370 |
Zbl 1332.65114
[17] Lessard, J.-P., James, J. D. Mireles, Ransford, J.:
Automatic differentiation for Fourier series and the radii polynomial approach. Physica D 334 (2016), 174-186.
DOI 10.1016/j.physd.2016.02.007 |
MR 3545977
[24] Sakaguchi, H., Brand, H. R.:
Stable localized solutions of arbitrary length for the quintic Swift-Hohenberg equation. Physica D 97 (1996), 274-285.
DOI 10.1016/0167-2789(96)00077-2
[25] Tucker, W.:
Validated Numerics. A Short Introduction to Rigorous Computations. Princeton University Press, Princeton (2011).
MR 2807595 |
Zbl 1231.65077
[26] Berg, J. B. van den, Groothedde, C. M., Lessard, J.-P.:
A general method for computer-assisted proofs of periodic solutions in delay differential problems. Preprint (2018).
MR 3896998
[31] Zgliczyński, P.:
Rigorous numerics for dissipative PDEs. III: An effective algorithm for rigorous integration of dissipative PDEs. Topol. Methods Nonlinear Anal. 36 (2010), 197-262.
MR 2788972 |
Zbl 1230.65113