  Structure-preserving algorithms for solving conservative PDEs with added
linear dissipation are generalized to systems with time-dependent
damping/driving terms. This study is motivated by several PDE models of
physical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schr\"{o}dinger,
and Camassa-Holm equations, all with damping/driving terms and time-dependent
coefficients. Since key features of the PDEs under consideration are described
by local conservation laws, which are independent of the boundary conditions,
the proposed (second-order in time) discretizations are developed with the
intent of preserving those local conservation laws. The methods are
respectively applied to a damped-driven nonlinear Schr\"{o}dinger equation and
a damped Camassa-Holm equation. Numerical experiments illustrate the
structure-preserving properties of the methods, as well as favorable results
over other competitive schemes.
