Supercomputer simulations of multiple-quantum dynamics of nuclear spins in solids

The effective algorithm is proposed for numerical solution of exactly solvable problems of intensities of multiple-quantum (MQ) coherences for one-dimensional systems of nuclear spins in solids. The detail description of the algorithm is given and it is shown its advantages in a comparison with other algorithms for such problems. The algorithm is realized as a program complex both for supercomputer systems with a flat RAM memory and for cluster ones with a distributed memory. The result of calculations of dynamics of a fifteen-spin system, which is described by the $2^{15}\times2^{15}$ matrix containing more than billion elements, is represented. The obtained results are applied to investigations of structures and dynamical processes in solids.