Fluid equations for a low-beta plasma, where the ratio of the kinetic to the magnetic pressure is small, constitute a system of parabolic partial-differential equations. Depending on the particular assumptions made, this may be a system of three equations for density, electron temperature, and ion temperature, or a single density equation, or a system of four equations where the current density or magnetic field also has to be determined. Such equations were previously solved by one-dimensional models, imposing some additional form of symmetry. In two dimensions, strongly anisotropic diffusion coefficients cause a spurious numerical loss of plasma. This problem was tackled in various geometries for the single density equation, and adequate mass conservation methods were developed. The two principal components of the diffusion were separated and, by a method of fractional steps, were treated by distinct methods. The diffusion parallel to the magnetic field was treated as a one-dimensional problem by two different techniques, (a) using a nonstandard Galerkin finite element, and (b) resulting from an averaging process across a flux tube. Meanwhile, the perpendicular diffusion, when treated by a Galerkin finite element method, gives rise to very wide band matrices, a problem that can be resolved advantageously by using the alternating direction implicit method.