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Occupation of an interval by self-replicating initial pulses is studiednumerically. Two different approximates in different categories are proposedfor the numerical solutions of some initial-boundary value problems. The sincdifferential quadrature combined with third-fourth order implicit Rosenbrockand exponential B-spline collocation methods are setup to obtain the numericalsolutions of the mentioned problems. The numerical simulations containingoccupation of single initial pulse, non or slow occupation model and coveringthe domain with two initial pulses are demonstrated by using both proposedmethods.

Motion of Patterns Modeled by the Gray-Scott Autocatalysis System in One Dimension