High order finite difference scheme for one dimensional heat transport equation at the microscale

Abstract EN

A sixth order compact difference scheme for space with Crank-Nicholson scheme for time is employed to solve one dimensional microscale heat transport equation.

The unconditionally stability of this new version of finite difference scheme is proved with respect to initial values.

Numerical experiments are introduced to test the accuracy of the sixth order compact finite differences and compare it with both the second order and fourth order difference schemes.

Our Numerical results showed that the sixth order compact scheme is computationally more efficient and more accurate than the second and fourth order schemes.