Abstract: A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

Key words: symplectic eigensolutions, Stokes flow, rectangular domain, Hamiltonian system, symplectic eigenvalues, hyperbolic heat conduction, sparse matrix, precise integration method, matrix exponential, fast algorithm