RK–Cayley Fehlberg method on homogeneous manifolds

A kind of explicit square conservation method to solve Landau–Lifshitz (LL) equation using the Lie group method was proposed. The method has the square conservation property and good accuracy using variable step size to control the error. We apply the method to the Landau–Lifshitz equation. Numerical experiment results show that the method can preserve the property of square conservation of LL equation and have good accuracy.