A predictor-corrector scheme for reaction-diffusion equations

Investigating the stability of two-dimensional laminar flow of an electrically conducting fluid (e.g. mercury) under the influence of a transverse magnetic field leads to a modified Orr-Sommerfeld problem, havining an additional term in the differential equation, which depends upon the Hartmann number M. For fixed M this problem is investigated depending upon the two parameters wave number α and Reynolds number R. Applying sufficient stability conditions stated in [5] boundaries of stability domains in the α, R-plane are obtained, where all eingenvalues λ satisfy Re λ > 0. For comparison in the α, R-plane boundary curves are shown which signify the onset of instability by including an eigenvalue λ having a negative real part.