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We present a new parallel supercomputer implementation of the Monte-Carlomethod for simulating the dynamical evolution of globular star clusters. Ourmethod is based on a modified version of Henon's Monte-Carlo algorithm forsolving the Fokker-Planck equation. Our code allows us to follow the evolutionof a cluster containing up to 5x10^5 stars to core collapse in < 40 hours ofcomputing time. In this paper we present the results of test calculations forclusters with equal-mass stars, starting from both Plummer and King modelinitial conditions. We consider isolated as well as tidally truncated clusters.Our results are compared to those obtained from approximate, self-similaranalytic solutions, from direct numerical integrations of the Fokker-Planckequation, and from direct N-body integrations performed on a GRAPE-4special-purpose computer with N=16384. In all cases we find excellent agreementwith other methods, establishing our new code as a robust tool for thenumerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio

Monte Carlo Simulations of Globular Cluster Evolution. I. Method and Test Calculations