Piecewise linear emulation of propagating fronts as a method for determining their speeds.
We use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations. The resulting analytic solution constitutes an excellent approximation to the exact propagating front, as is explicitly shown in the case of cubic and quintic nonlinearities, yielding also the correct value for the physically selected speed of the observable front. Such a piecewise linear emulation can be used for any nonlinearity, giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states, especially pushed fronts.
Theodorakis
Stavros
S
Physics Department, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus. stavrost@ucy.ac.cy
Svoukis
Efthymios
E