  Occupation of an interval by self-replicating initial pulses is studied
numerically. Two different approximates in different categories are proposed
for the numerical solutions of some initial-boundary value problems. The sinc
differential quadrature combined with third-fourth order implicit Rosenbrock
and exponential B-spline collocation methods are setup to obtain the numerical
solutions of the mentioned problems. The numerical simulations containing
occupation of single initial pulse, non or slow occupation model and covering
the domain with two initial pulses are demonstrated by using both proposed
methods.
