2014
DOI: 10.5539/jmr.v6n2p18
|View full text |Cite
|
Sign up to set email alerts
|

The Second Lie-Group $SO_o(n,1)$ Used to Solve Ordinary Differential Equations

Abstract: Liu (2001) derived the first augmented Lie-group S O o (n, 1) symmetry for the nonlinear ordinary differential equations (ODEs):ẋ = f(x, t), and developed the corresponding group-preserving scheme (GPS). However, the earlier formulation did not consider the rotational effect of nonlinear ODEs. In this paper, we derive the second augmented Lie-group S O o (n, 1) symmetry by taking the rotational effect into account. The numerical algorithm exhibits two solutions of the Lie-group G ∈ S O o (n, 1), depending on t… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2015
2015
2020
2020

Publication Types

Select...
2

Relationship

1
1

Authors

Journals

citations
Cited by 2 publications
(2 citation statements)
references
References 23 publications
0
2
0
Order By: Relevance
“…x x is the Euclidean norm of x, and the dot between two vectors, say ⋅ x y , denotes the inner product of x and y. Then we can derive [9]…”
Section: A System Formulationmentioning
confidence: 99%
See 1 more Smart Citation
“…x x is the Euclidean norm of x, and the dot between two vectors, say ⋅ x y , denotes the inner product of x and y. Then we can derive [9]…”
Section: A System Formulationmentioning
confidence: 99%
“…there exist two different types solutions of (z, w, y). Here, we do not give a detailed derivation of the solutions for (z, w, y) and the corresponding second generation group preserving scheme (GPS2), but the reader can refer [9]- [11].…”
Section: Two Branches Solutionsmentioning
confidence: 99%