  We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) +
f(y(t)) with energy conservation. Such conservative models appear for instance
in quantum physics, engineering and molecular dynamics. A new class of
energy-preserving schemes is constructed by the ideas of scalar auxiliary
variable (SAV) and splitting, from which the nonlinearly implicit schemes have
been improved to be linearly implicit. The energy conservation and error
estimates are rigorously derived. Based on these results, it is shown that the
new proposed schemes have unconditionally energy stability and can be
implemented with a cost of solving a linearly implicit system. Numerical
experiments are done to confirm these good features of the new schemes.
