A class of volume-preserving numerical algorithms

In this paper, a class of more general volume-preserving mappings which can include two classes of existing volume-preserving mappings, is presented. Associated with these volume-preserving mappings, we get the corresponding generating functions. Since these generating functions satisfy the generalized Hamilton-Jacobi (GHJ) equations, the higher-order volume-preserving numerical algorithms are obtained by solving the GHJ equations.