Approximately preserving symmetries in the
numerical integration of ordinary differential equations
1999 ◽
Vol 10
(5)
◽
pp. 419-445
◽
Keyword(s):
We present a general procedure for recursively improving the invariance of a numerical integrator under a symmetry group. If h is a symmetry, we construct the adjoint method h−1h. In each time step we apply either the original method or the adjoint method, according to a prescription based on the Thue–Morse sequence. The outcome is a solution sequence which displays progressively smaller symmetry errors, to any desired order in the time-step. The method can also be used to force the solution to stay close to a desired submanifold of phase space, while retaining structural properties of the original method.
1978 ◽
Vol 41
◽
pp. 159-173
2020 ◽
Vol 501
(1)
◽
pp. 1511-1519
Keyword(s):
1963 ◽
Vol 3
(2)
◽
pp. 336-350
◽
1985 ◽
Vol 22
(6)
◽
pp. 1153-1166
◽