  The classic second-order average vector field (AVF) method can exactly
preserve the energy for Hamiltonian ordinary differential equations and partial
differential equations. However, the AVF method inevitably leads to
fully-implicit nonlinear algebraic equations for general nonlinear systems. To
address this drawback and maintain the desired energy-preserving property, a
first-order partitioned AVF method is proposed which first divides the
variables into groups and then applies the AVF method step by step. In
conjunction with its adjoint method we present the partitioned AVF composition
method and plus method respectively to improve its accuracy to second order.
Concrete schemes for two classic model equations are constructed with
semi-implicit, linear-implicit properties that make considerable lower cost
than the original AVF method. Furthermore, additional conservative property can
be generated besides the conventional energy preservation for specific
problems. Numerical verification of these schemes further conforms our results.
