Preserving algebraic invariants with Runge-Kutta methods
The authors introduce a generalized class of Runge-Kutta schemes, namely Lie-group-type Runge-Kutta methods, designed to solve ordinary differential equations on Lie groups, and to preserve a large class of algebraic invariants. The conditions for the retention of algebraic invariants are imposed on the coefficients of the methods and a pair of partial differential equations that must be obeyed by the invariants. It is also proved that Runge-Kutta schemes cannot preserve any polynomial conservation law except for linear and quadratic.
scientific article; zbMATH DE number 1566003
scientific article