The Study Of Stability For Four Numerical Schemes With Multilevel W-like Incremental Unknowns

In this article,we introduce the multilevel W-like incremental unknowns for the implementation of nonlinear Galerkin method when finite differences are used for the space discretization. The four new numerical schemes for reaction-diffusion equations are presented and analyzed. The stability conditions of these schemes are compared carefully. Particularly, the stability conditions of semi-implicit and weighted semi-implicit schemes are improved obviously when compared with the explicit scheme of M.Chen and R.Temam. When the nonlinear effect is strong, the stability condition are comparable to their implicit scheme, but the complexity of the computation in each time step are improved. Furthermore we find the stability condition is best when in the weighted semi-implicit schemes.Otherwise, the method is discussed in two and three dimensional space in this paper.