comparison of an implicit vs. explicit one-dimensional finite differences program for solving the unsteady heat-flow-equation

The heat-flow equation (without source-term):

The input data-file (identical for both programs)

The explicit version (Fortran 77 source code)

The implict version (Fortran 77 source code)

A small programm for comparison of the results (Fortran 77 source code)

New and nicer the same programs as scilab programs: explict, implicit (updated at 2012-03-07).

The programs calculate the heat distribution at a 100m long row in one year, where the row has the following thermal properties:

• Heat conduction = 1.5 (W/(K m))
• Density * specific heat = 1,380,000 (J/(m³ M))
• The time step is in both cases 1 hour
• Initial temperature = 283.15 K
• Spatial step size 1 m
• At the first 3 grid nodes there is a Dirichlet border condition with a T of 283.15 + 50 (K)

The results:

Explicit

Implicit

The difference

(really small - only at the borders there is a bigger difference probably because of a malfunction of the SY-Subroutine):