<Abstrcat> A simple and practical direct alternative format for calculation of the characteristic line equations and boundary condition equations of pump-failure water-hammer were proposed.

A simple and practical direct alternative format for calculation of the characteristic line equations and boundary condition equations of pump-failure water-hammer was proposed.

Based on the geometrical meaning of structural reliability index, the direct iteration calculation of a nonlinear function under the condition of correlated variables was discussed by using coordinate transformation and matrix operation.

In this paper,Ishikawa iterative schemes with mixed errors are studied,method of proof and technique are improved.

By making use of monotone iterative technique,the iterative scheme and existence theorem of positive solution are established for a nonlinear second-order boundary value system.

For the problems of one-dimensional and two-dimension iteration, this text compares the convergence and convergence rate of different iteration formats, and provides suggestions to the formation of iteration format.

In this paper,an iterative method is given to solve the equations with non-differential terms.

A iteration scheme of solving zeros of nonlinear functions and its convergence;

The accurate iteration scheme for zero points of m-accretive mappings,introduced by Chidume and Zegeye has been essentially extended to the case of iteration scheme with errors.

The accurate iteration scheme for zero points of m-accretive mappings introduced by Chidume and Zegeye in 2002 has been essentially extended.