To solve complex systems obtained from 2D nonlinear Schrödinger equation, a method of high-order PCG coupling with BICG has been developed. Meanwhile, the complex systems of order M can be reconstructed as the real systems of order 2M. From the theory of order matrix, the high order approximate LU decompositions are given as the preconditioners to solve the real systems. Numerical results show that the computational efficiency can be nearly doubled by the high-order PCG method comparing with the ICCG method.

For the computation of saturated-unsaturated water table flow, a kind of difference scheme of irregular convex polygon mesh is developed. Using this method, saturated-unsaturated seepage flow is calculated to AKAI's sand model and KOM-ADA's reservoir model. The results obtained here are compared with results ob -tained from computations in which rectangled difference meshes were used. The applicableness and accuracy of this method are also discussed.

For saturated-unsaturated water table flow, computations of ADEP, ADIP and implicitly alternating direction iterative procedure are made and compared.The i-terations are not convergent and computational results are strongly distortional Based on supplementing a particular term, a kind of completely implicit and altern-ting direction iterative procedure is given The relative results for computational model of different scales are satisfactory. Problems of how to give the particular supplemental term and how to select better parameters are discussed, the computational results are given.

The implicit alternating-direction-iteration method is used to solve question of saturated-unsaturated seepage flow under rapid change of the water surface level. The numerical.results of Akai model are given and compared with experimental results.It is found that the numerical results given in this paper are in good agreement with experimental results and better than results by finite element method.The numerical results of komada model are close to results by finite element method.