Fourth order compact finite difference scheme for two-dimensional microscale heat equation

Abstract EN

In this paper, fourth order compact difference scheme is employed to solve two dimensional microscale heat transport equation.

By introducing an intermediate function for the heat transport equation, we use the fourth order compact scheme for the space with a second order Crank-Nicolson scheme for the time.

The stability of this scheme is proved unconditionally stable with respect to initial values.

The computational accuracy is demonstrated that the results of the compact fourth order finite difference scheme is more accurate than the second order finite difference scheme [12].