High accuracy stable numerical solution of 1D microscale heat transport equation

We investigate the use of a fourth-order compact finite difference scheme f or solving a one-dimensional heat transport equation at the microscale. The fourth-order compact scheme is used with a Crank-Nicholson type integrator by introducing an intermediate function for the heat transport equation. T he new scheme is proved to be unconditionally stable with respect to initia l values. Numerical experiments are conducted to compare the new scheme wit h the existing scheme based on second-order spatial discretization. It is s hown that the new scheme is computationally more efficient and more accurat e than the second-order scheme. Copyright (C) 2001 John Wiley & Sons, Ltd.