Numerical solution of reactive-diffusive systems

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Abstract
Seven explicit numerical procedures are employed to calculate the propagation of a one-dimensional wave which is governed by a reaction-diffusion equation. Comparisons amongst the methods are presented 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 and computed wave speed. It is shown that a second-order accurate, in both space and time, explicit predictor-corrector method produces the least L 2-norm errors. It is also shown that a modified Saul'yev average scheme yields the most accurate and constant wave speed.