A novel algorithm for calculating a brass instrument's acoustic pressure response to an impulsive volume flow at the input end [R. D. Ayers, J. Acoust. Soc. Am. 100, 1190--1198 (1996)] is applied to sound simulation. The algorithm employs several impulse responses that have no multiple reflections and that decay very rapidly. These are convolved with the mouthpiece pressure and volume flow in the past to give the pressure at the present. The impulse responses calculated from the measured dimensions of an actual B(flat) trumpet can be considered for simulation purposes as being confined in a period of 13 ms, which is four times shorter than the nonzero period of the reflection function used in the conventional algorithm. Due to the shorter convolution time, the new algorithm, incorporated with a nonlinear driver model of lip vibration and airflow, can run about 4.5 times faster than the method using the reflection function. Simulations with the two algorithms indicate the same behavior for the transition among the air-column resonance modes. Individual waveforms synthesized with the new algorithm are in very good agreement with their counterparts synthesized with the conventional algorithm.