  In this paper, a centred universal high-order finite volume method for
solving hyperbolic balance laws is presented. The scheme belongs to the family
of ADER methods where the Generalized Riemann Problems (GRP) is a building
block. The solution to these problems is carried through an implicit Taylor
series expansion, which allows the scheme to works very well for stiff source
terms. A von Neumann stability analysis is carried out to investigate the range
of CFL values for which stability and accuracy are balanced. The scheme
implements a centred, low dissipation approach for dealing with the advective
part of the system which profits from small CFL values. Numerical tests
demonstrate that the present scheme can solve, efficiently, hyperbolic balance
laws in both conservative and non-conservative form as well. An empirical
convergence rate assessment shows that the expected theoretical orders of
accuracy are achieved up to the fifth order.
