  Two-fluid ideal plasma equations are a generalized form of the ideal MHD
equations in which electrons and ions are considered as separate species. The
design of efficient numerical schemes for the these equations is complicated on
account of their non-linear nature and the presence of stiff source terms,
especially for high charge to mass ratios and for low Larmor radii. In this
article, we design entropy stable finite difference schemes for the two-fluid
equations by combining entropy conservative fluxes and suitable numerical
diffusion operators. Furthermore, to overcome the time step restrictions
imposed by the stiff source terms, we devise time-stepping routines based on
implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the
two-fluid plasma equations is exploited by us to design IMEX schemes in which
only local (in each cell) linear equations need to be solved at each time step.
Benchmark numerical experiments are presented to illustrate the robustness and
accuracy of these schemes.
