Article: Square-Conservative Schemes for a Class of Evolution Equations Using Lie-Group Methods
Author: J-B Chen, H Munthe-Kaas, M-Z Qin
Journal: SIAM J. NUMER. ANAL. Vol. 39, No. 6, pp. 2164–2178 (2002).
Abstract: A new method for constructing square-conservative schemes for a class of evolution equations using Lie-group methods is presented. The basic idea is as follows. First, we discretize the space variable appropriately so that the resulting semidiscrete system of equations can be cast into a system of ordinary differential equations evolving on a sphere. Second, we apply Lie-group methods to the semidiscrete system, and then square-conservative schemes can be constructed since the obtained numerical solution evolves on the same sphere. Both exponential and Cayley coordinates are used. Numerical experiments are also reported.
Remarks in hindsight: None yet.
22 Jan 2001