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Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
R. Castelli, M. Gameiro and J.-P. Lessard
Archive for Rational Mechanics and Analysis, 228(1):129–157, 2018
PDF arXiv:1509.08648 doi:10.1007/s00205-017-1186-0 Publication [37]
Files
Codes and data accompanying the paper, reproducing the computer-assisted proofs it reports.
- codes.zip (347 KB)
codes/ — 20 files (344 KB)
- fft_data.mat (227 KB)
- padding.m (245 B)
- script_proof_theorem_1.m (1002 B)
- script_proof_theorem_2.m (1002 B)
- script_proof_theorem_3.m (1002 B)
- script_proof_theorem_4.m (1002 B)
- validate_boussinesq_sym_int.m (7.1 KB)
- verifyfft.m (2.3 KB)
- solutions/sol_1_branch_1.mat (2.3 KB)
- solutions/sol_1_branch_2.mat (2.3 KB)
- solutions/sol_1_branch_3.mat (3.4 KB)
- solutions/sol_1_branch_4.mat (2.3 KB)
- solutions/sol_25_branch_1.mat (12 KB)
- solutions/sol_25_branch_2.mat (3.4 KB)
- solutions/sol_25_branch_3.mat (10 KB)
- solutions/sol_25_branch_4.mat (7.2 KB)
- solutions/sol_50_branch_1.mat (29 KB)
- solutions/sol_50_branch_2.mat (4.0 KB)
- solutions/sol_50_branch_3.mat (15 KB)
- solutions/sol_50_branch_4.mat (11 KB)
The scripts are written in MATLAB; the rigorous parts require the interval arithmetic package INTLAB to be installed and started.