Bespoke finite difference schemes that preserve multiple conservation laws
2015 ◽
Vol 18
(1)
◽
pp. 372-403
◽
Keyword(s):
Conservation laws provide important constraints on the solutions of partial differential equations (PDEs), therefore it is important to preserve them when discretizing such equations. In this paper, a new systematic method for discretizing a PDE, so as to preserve the local form of multiple conservation laws, is presented. The technique, which uses symbolic computation, is applied to the Korteweg–de Vries (KdV) equation to find novel explicit and implicit schemes that have finite difference analogues of its first and second conservation laws and its first and third conservation laws. The resulting schemes are numerically compared with a multisymplectic scheme.
2001 ◽
Vol 77
(1)
◽
pp. 135-144
◽
2014 ◽
Vol 94
(11)
◽
pp. 974-974
2011 ◽
Vol 179
(1)
◽
pp. 100-126
◽
1999 ◽
Vol 07
(01)
◽
pp. 39-58
◽
2016 ◽
Vol 54
(1)
◽
pp. 86-119
◽
2010 ◽
Vol 42
(5)
◽
pp. 2275-2296
◽