解模守恒微分方程的显式平方守恒格式

对具有模守恒的微分方程，经典的显式Runge—Kutta方法和线性多步方法不能保微分方程的模守恒特性．我们利用李群算法和Cayley变换构造了高阶显式平方守恒格式，应用到模守恒的微分方程如Euler方程，Landau—Lifshitz方程，并且与相同阶的显式Runge—Kutta方法在保模守恒和精度方面进行了比较，数值结果表明用李群算法构造的新的显式平方守恒格式能保微分方程模守恒的特性且它和相应Runge—Kutta方法有相同的精度．

EXPLICIT SQUARE CONSERVATION SCHEME FOR MODULUS CONSERVING DIFFERENTIAL EQUATIONS

To modulus conserving differential equations, classical explicit Runge-Kutta method and linear multi-step method can not preserve the modulus of the differential equation. We apply Lie group method and Cayley transformation to construct high order explicit square conserving scheme for the modulus conserving differential equations, such as the Euler equation, the Landau-Lifshitz equation and compare the numerical results with the classical Runge-Kutta method in modulus conserving and accuracy. Numerical experiments results show that the new explicit square conserving scheme can preserve the modulus conserving property and the same accuracy as the corresponding classical Runge-Kutta methods.