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Extending investigations of Barker, Humpherys, Lafitte, Rudd, and Zumbrun forcompressible gas dynamics and Freist\"uhler and Trakhinin for compressiblemagnetohydrodynamics, we study by a combination of asymptotic ODE estimates andnumerical Evans function computations the one-dimensional stability of parallelisentropic magnetohydrodynamic shock layers over the full range of physicalparameters (shock amplitude, strength of imposed magnetic field, viscosity,magnetic permeability, and electrical resistivity) for a $\gamma$-law gas with$\gamma\in [1,3]$. Other $\gamma$-values may be treated similarly, but were notchecked numerically. Depending on magnetic field strength, these shocks may beof fast Lax, intermediate (overcompressive), or slow Lax type; however, theshock layer is independent of magnetic field, consisting of a purelygas-dynamical profile. In each case, our results indicate stability.Interesting features of the analysis are the need to renormalize the Evansfunction in order to pass continuously across parameter values where the shockchanges type or toward the large-amplitude limit at frequency $\lambda=0$ andthe systematic use of winding number computations on Riemann surfaces.

One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamic