  We analyze the multisymplectic Preissman scheme for the KdV equation with the
periodic boundary condition and show that the unconvergence of the widely-used
iterative methods to solve the resulting nonlinear algebra system of the
Preissman scheme is due to the introduced potential function. A artificial
numerical condition is added to the periodic boundary condition. The added
boundary condition makes the numerical implementation of the multisymplectic
Preissman scheme practical and is proved not to change the numerical solutions
of the KdV equation. Based on our analysis, we derive some new schemes which
are not restricted by the artificial boundary condition and more efficient than
the Preissman scheme because of less computing cost and less computer storages.
By eliminating the auxiliary variables, we also derive two schemes for the KdV
equation, one is a 12-point scheme and the other is an 8-point scheme. As the
byproducts, we present two new explicit schemes which are not multisymplectic
but still have remarkable numerical stable property.
