High accuracy difference scheme for seepage problem

Among the classical difference schemes for seepage, the Crank Nicolson scheme is only of 2 order accuracy on it.Based on the concept of ultraconvergence point of derivative, a new difference scheme, which is of 3 order accuracy in t, is propssed in this paper.For the purpose to improve the stable, convergence condition, the composite difference scheme based on linear superposition of 3 order accuracy scheme and explicit scheme is also proposed.Resultsof calculation example show that the advantages of the composite difference scheme are high accuracy, loose limitation of stability and convergence, easy programming and so on.