  Modified Patankar schemes are linearly implicit time integration methods
designed to be unconditionally positive and conservative. In the present work
we extend the Patankar-type approach to linear multistep methods and prove that
the resulting discretizations retain, with no restrictions on the step size,
the positivity of the solution and the linear invariant of the continuous-time
system. Moreover, we provide results on arbitrarily high order of convergence
and we introduce an embedding technique for the Patankar weight denominators to
achieve it.
