  We present a fourth-order finite-volume algorithm in space and time for low
Mach number reacting flow with detailed kinetics and transport. Our temporal
integration scheme is based on a multi-implicit spectral deferred correction
(MISDC) strategy that iteratively couples advection, diffusion, and reactions
evolving subject to a constraint. Our new approach overcomes a stability
limitation of our previous second-order method encountered when trying to
incorporate higher-order polynomial representations of the solution in time to
increase accuracy. We have developed a new iterative scheme that naturally fits
within our MISDC framework that allows us to simultaneously conserve mass and
energy while satisfying on the equation of state. We analyse the conditions for
which the iterative schemes are guaranteed to converge to the fixed point
solution. We present numerical examples illustrating the performance of the new
method on premixed hydrogen, methane, and dimethyl ether flames.
