  We present a class of hybrid FD-FV (finite difference and finite volume)
methods for solving general hyperbolic conservation laws written in first-order
form. The presentation focuses on one- and two-dimensional Cartesian grids;
however, the generalization to higher dimensions is straightforward. These
methods use both cell-averaged values and nodal values as dependent variables
to discretize the governing partial differential equation (PDE) in space, and
they are combined with method of lines for integration in time. This framework
is absent of any Riemann solvers while it achieves numerical conservation
naturally. This paper focuses on the accuracy and linear stability of the
proposed FD-FV methods, thus we suppose in addition that the solutions are
sufficiently smooth. In particular, we prove that the spatial-order of the
FD-FV method is typically one-order higher than that of the discrete
differential operator, which is involved in the construction of the method. In
addition, the methods are linearly stable subjected to a Courant-Friedrich-Lewy
condition when appropriate time-integrators are used. The numerical performance
of the methods is assessed by a number of benchmark problems in one and two
dimensions. These examples include the linear advection equation, nonlinear
Euler equations, the solid dynamics problem for linear elastic orthotropic
materials, and the Buckley-Leverett equation.
