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Article overview
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Structure preserving discretizations of the Liouville equation and their numerical tests | | D. Levi
; L. Martina
; P. Winternitz
; | | Date: |
8 Apr 2015 | | Abstract: | The main purpose of this article is to show how structure reflected in
partial differential equations can be preserved in a discrete world and
reflected in difference schemes.
Three different structure preserving discretizations of the Liouville
equation are presented and then used to solve specific boundary value problems.
The results are compared with exact solutions satisfying the same boundary
conditions. All three discretizations are on four point lattices. One preserves
linearizability of the equation, another the infinite dimensional symmetry
group as higher symmetries, the third preserves the maximal finite dimensional
subgroup of the symmetry group as point symmetries. A 9-point invariant scheme
that gives a better approximation of the equation, but worse numerical results
for solutions is presented and discussed. | | Source: | arXiv, 1504.1953 | | Services: | Forum | Review | PDF | Favorites | |
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