  The linear perturbation equation of the tearing instability derived in LSC
theory (Loureiro, Schekochihin, and Cowley, PoP2007) is numerically examined as
an initial value problem, where the inner and outer regions are seamlessly
solved under uniform resistivity. Hence, all regions are solved as the
resistive MHD (magnetohydrodynamics). To comprehensively study physically
acceptable perturbation solutions, the behaviors of the local maximum points
required for physically acceptable solutions and zero-crossing points, at which
\phi=0 and \psi=0, are examined. Eventually, the uniform resistivity assumed in
the outer region is shown to play an important role in improving some
conclusions derived from the theory. In conclusion, the upper limit
\lambda_{up} of the growth rate obtained in the improved (modified) LSC theory
is shown to be regulated by the Alfven speed measured in the outer region. It
is also shown to be partially consistent with the growth rate in the linear
developing stage of the impulsive tearing instability observed in the
compressible MHD simulation of the plasmoid instability (PI) based on uniform
resistivity.
