## ON THE LIE ALGEBRAIC SOLUTION OF THE DIFFERENTIAL EQUATIONS d U/ d T=H·U

**Lee Deqian Huang Zhongtao (Dept. of Appl. Math., South China Univ of Tech)**

A method to seek the solution U(t) of the linear differential equations d U/ d t= H(t)·U(t) has been described by James Wei and Edward Norman . Their method is based on the theory of Lie algebras. In this paper, the structure of the solution to the equation d U/ d t= H(t)·U(t) , U(0)=I, is being discussed. Where U is time dependent linear operator in a finite dimensional space and H(t)=b 1(t)H 1+b 2(t)H 2+……+b m-1 (t)H m-1 +b m(t)H m. If the Lie algera L generated by {H 1,H 2,…,H m-1 ,H m} is solvable, then we can reduce its solution U(t)= exp {f 1(t)H 1} exp {f 2(t)H 2}…… exp {f m(t)H m} to a matrix in which all elements are elementary functions of g i. Finally, the reduction method is illustrated in two examples.

【CateGory Index】：
O152.5

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