  We present a family of multistep integrators based on the Adams-Bashforth
methods. These schemes can be constructed for arbitrary convergence order with
arbitrary step size variation. The step size can differ between different
subdomains of the system. It can also change with time within a given
subdomain. The methods are linearly conservative, preserving a wide class of
analytically constant quantities to numerical roundoff, even when numerical
truncation error is significantly higher. These methods are intended for use in
solving conservative PDEs in discontinuous Galerkin formulations or in
finite-difference methods with compact stencils. A numerical test demonstrates
these properties and shows that significant speed improvements over the
standard Adams-Bashforth schemes can be obtained.
