A dynamical storage/deletion algorithm with nodal deletion and global deletion modes, originally based on the in situ adaptive tabulation technique, is proposed to accelerate chemistry computations in reactive flows with high Mach number. The algorithm allows for the approximations of the chemical reaction through retrieving nodes stored in a table and deleting nodes during computations. The algorithm is applied to the C3H8/air detonation induced by shock wave focusing. The computational results show the potential advantage of the node removal or table deletion in the simulation of multi-dimensional unsteady detonations. The nodal deletion mode proposed in the present work has a higher speed-up factor of computations than the global deletion mode due to the reservation of nodes, which has a high retrieval frequency in the table. At the specified error tolerance of node approximation, the efficiency of algorithm is dependent on the deletion modes and the table size, without losing the computational accuracy.