  In this article we develop a Primitive Variable Recovery Scheme (PVRS) to
solve any system of coupled differential conservative equations. This method
obtains directly the primitive variables applying the chain rule to the time
term of the conservative equations. With this, a traditional finite volume
method for the flux is applied in order avoid violation of both, the entropy
and "Rankine-Hugoniot" jump conditions. The time evolution is then computed
using a forward finite difference scheme. This numerical technique evades the
recovery of the primitive vector by solving an algebraic system of equations as
it is often used and so, it generalises standard techniques to solve these kind
of coupled systems. The article is presented bearing in mind special
relativistic hydrodynamic numerical schemes with an added pedagogical view in
the appendix section in order to easily comprehend the PVRS. We present the
convergence of the method for standard shock-tube problems of special
relativistic hydrodynamics and a graphical visualisation of the errors using
the fluctuations of the numerical values with respect to exact analytic
solutions. The PVRS circumvents the sometimes arduous computation that arises
from standard numerical methods techniques, which obtain the desired primitive
vector solution through an algebraic polynomial of the charges.
