On Cayley-Transform Methods for the Discretization of Lie-Group Equations
β Scribed by A. Iserles
- Publisher
- Springer-Verlag
- Year
- 2001
- Tongue
- English
- Weight
- 212 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1615-3375
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π SIMILAR VOLUMES
## a b s t r a c t For the Bratu problem, we transform it into a non-linear second order boundary value problem, and then solve it by the Lie-group shooting method (LGSM). LGSM allows us to search a missing initial slope and moreover, the initial slope can be expressed as a function of r 2 [0, 1],
This note deals with the numerical solution of the matrix differential system where Y0 is a real constant symmetric matrix, B maps symmetric into skew-symmetric matrices, and [B(t, Y), Y] is the Lie bracket commutator of B(t, Y) and Y, i.e. [B(t, Y), Y] = B(t, Y)Y -YB(t, Y). The unique solution of
We consider the operator equation SX -~)~t i U, XV, = Y where { U, }. { t~ } are some commutative sets of operators but in general { U, } need not commute with { 1,)}. Particular cases of this equation are the Syivester and Ljaptmov equations. We give a new representation and an approximation of the