An economical difference scheme for heat transport equation at the microscale

Heat transport at the microscale is of vital importance in microtechnology applications. In this article, we proposed a new ADI difference scheme of the Crank‐Nicholson type for heat transport equation at the microscale. It is shown that the scheme is second order accurate in time and in space in the H¹ norm. Numerical result implies that the theoretical analysis is correct and the scheme is effective. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004