Unconditionally stable finite difference scheme and iterative solution of 2D microscale heat transport equation

A two-dimensional time-dependent heat transport equation at the microscale is derived. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference sche me is proved. A computational procedure is designed to solve the discretize d linear system at each time step by using a preconditioned conjugate gradi ent method. Numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure. (C) 2001 Academic Press.