Abstract: The precise time integration (PTI) proposed for transient linear system can give almost accurate numerical results at the integration point. But when the dimensions of the system is very large, the computational efficiency is a big problem. In this paper, the symmetry of tile exponential matrix in the precise time integration for transient heat conduction is obtained by employing some transformation. Using this symmetry, the computational amount and the storage of PTI can be reduced nearly 50%. Moreover,...