Accurate one-dimensional computation of frontal phenomena by PLIM

We introduce a new method for solving systems of one-dimensional hyperbolic partial differential equations and present the first applications of this method. The piecewise linear interpolation method PLIM is shown to have the capability to preserve the shape of a propagating distribution and great applicability. Various difficult flow problems, such as the strong convection problem, the convection diffusion problem, and the reaction-diffusion problem, have been solved. In addition, the approximate hyperbolic equations technique (AHET) to handle the diffusion terms is introduced.