A modified stochastic perturbation method for stochastic hyperbolic heat conduction problems

The stochastic hyperbolic heat conduction problem is addressed. The random field is approximated by using the Karhunen-Loeve expansion truncated after a finite numbers of terms, and a modified stochastic perturbation method (MSPM) is proposed for the stochastic hyperbolic heat conduction problems. The MSPM is based on the stochastic perturbation theory, and can provide the mean and covariance of the random temperature including some third- and forth-order terms. Compared with the original stochastic perturbation method, the MSPM is more accurate and is more convenient for the numerical implementation, and hence is more applicable for the stochastic hyperbolic heat conduction problem. Two numerical examples demonstrate that the proposed method can provide very accurate results and can be used for the stochastic hyperbolic heat conduction problems.