In order to increase the time delay of Brillouin slow light and decrease its pulse broadening

fiber-based Stimulated Brillouin Scattering（SBS） coupled equations are numerically solved by using the upwind scheme-based finite difference method and

when continuous light with slowly changing rising edge is used as the pump light

the changes of the time delay and pulse broadening factors of Stokes light at the fiber output end with gain are analyzed.Numerical results indicate that such a pump light can increase the time delay of long Gaussian pulses（FWHM=120 ns） up to 52 ns and that of short Gaussian pulses（FWHM=20 ns） up to 64 ns and at the same time reduce the pulse broadening of long and short Gaussian pulses.