Line Integral Methods for Conservative Problems
Gallery
of problems taken from Chapters 2, 4, 5, and 6 of the book
(for each problem, there is the plot of the solution and of the error in the numerical Hamiltonian)
of problems taken from Chapters 2, 4, 5, and 6 of the book
(for each problem, there is the plot of the solution and of the error in the numerical Hamiltonian)
| Kepler problem with eccentricity e=0.6. HBVM(8,2) 1000 steps with constant stepsize h=2*pi/100 |
Cassini problem HBVM(4,2) 300 steps with constant stepsize h=T/100 T=3.131990057003955 is the period |
Fermi-Pasta-Ulam problem 7 masses with constants [10,10,10,1e4,10,10,10] HBVM(4,2) 1000 steps with constant stepsize h=0.1 |
| Henon-Heiles problem trajectory inside the invariant region (triangle) HBVM(3,2) 1000 steps with constant stepsize h=1 |
Nonlinear pendulum problem periodic solution close to the homoclinic orbit HBVM(8,2) 400 steps with constant stepsize h=0.5 |
Frozen argon crystal problem 7 atoms crystal HBVM(8,2) 10000 steps with constant stepsize h=1e-4 |
| Planar circular restricted three-body problem (i.e., the logo) HBVM(9,3) variable stepsize integration in the interval [0,100] with tolerance tol=1e-10 |
Sine-Gordon partial differential equation double-pole soliton in [-20,20]x[0,100] HBVM(5,1) with Fourier-Galerkin space discretization (N=100, m=200) 1000 steps with constant stepsize h=0.1 |
Hill boundary value problem HBVM(3,1) 50 steps with constant stepsize h=T/50, with T={0.1,1.4,2.5,3} the trajectory end time |