Jennifer J. Zhao
Department of Mathematics and Statistics
University of Michigan at Dearborn
Dearborn, MI 48128-1491, USA
Numerical computation techniques are proposed to solve a three dimensional time dependent microscale heat transport equation. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to solve the resulting sparse linear system at each time step with a few iterative methods and their performances are compared experimentally. Numerical experiments are presented to demonstrate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure.
Mathematics Subject Classification: 65M06, 65N12.