  A new approach using a hyperbolic-equation system (HES) is proposed to solve
for the electron fluids in quasi-neutral plasmas. The HES approach avoids
treatments of cross-diffusion terms which cause numerical instabilities in
conventional approaches using an elliptic equation (EE). A test calculation
reveals that the HES approach can robustly solve problems of strong magnetic
confinement by using an upwind method. The computation time of the HES approach
is compared with that of the EE approach in terms of the size of the problem
and the strength of magnetic confinement. The results indicate that the HES
approach can be used to solve problems in a simple structured mesh without
increasing computational time compared to the EE approach and that it features
fast convergence in conditions of strong magnetic confinement.
