A variable time step integration algorithm for carrying out molecular dynamics simulations of atomic collision cascades is proposed which evaluates the interaction forces only once per time step. The algorithm is tested on some model problems which have exact solutions and is compared against other common methods. These comparisons show that the method has good stability and accuracy. Applications to Ar+ bombardment of Cu and Si show good accuracy and improved speed to the original method [D. E. Harrison, W. L. Gay, and H. M. Effron, J. Math. Phys. 10, 1179 (1969)].

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