Linear conservation laws for ODEs

Some physical systems described by ODEs have quantities that are conserved as the system evolves. Runge-Kutta formulas and linear multistep methods preserve linear conservation laws automatically. A code for the integration of ODEs involves a number of algorithms in addition to the basic formula. It is shown here that popular codes preserve linear conservation laws if they are used properly. An application is made to differential-algebraic equations of index 2 arising in the solution of the Navier-Stokes equation by the method of lines.