Square-conservative schemes for a class of evolution equations using Lie-group methods

摘要

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. [References: 15]