Abstract: In order to solve a class of evolution equaiton u_t=au2K+1(where a is constant, u_2K+1=∂^2K+1/∂x_2K+1,K=l,2,……) two classes of explicit difference schemes with higher stability properties are constituted. And two classes of semi -explicit difference schemes are also established by introducing a dissipative term, they are unconditionally stable and can be calculated explicitly.

Key words: dissipative term, fourier analysis, semi-explicit and explicit schemes, evolution equation