Numerical solution of reactive-diffusive systems

TLDR: In this paper, four time linearization techniques and two operator-splitting algorithms have been employed to study the propagation of a one-dimensional wave governed by a reaction-diffusion equation.

Abstract: Four time linearization techniques and two operator-splitting algorithms have been employed to study the propagation of a one-dimensional wave governed by a reaction-diffusion equation. Comparisons amongst the methods are shown in terms of the L 2-norm error and computed wave speeds. The calculations have been performed with different numerical grids in order to determine the effects of the temporal and spatial step sizes on the accuracy. It is shown that a time linearization procedure with a second-order accurate temporal approximation and a fourth-order accurate spatial discretization yields the most accurate results. The numerical calculations are compared with those reported in Parts 1 and 2. It is concluded that the most accurate time linearization method described in this paper offers a great promise for the computation of multi-dimensional reaction-diffusion equations.