Finite Difference Method for Elliptic Equations

The finite difference method is easy to program in Excel, provided the equation is not too complicated. Solving the problem in Excel does require solving it more than once, though, to assess the accuracy. As an example, take the heat conduction equation with a heat generation term, Eq. (F.48)  

You copy this equation for every internal grid point, set the boundary equations, and turn on the iteration feature to obtaing the solution. Then you have to do it again with a finer mesh to assess the accuracy. If the heat generation term depends upon temperature, it is easy to include that complication just by inserting the formula in place of A 2. 

This appendix gives a brief overview of the methods that are preprogrammed in the software packages Excel, MATLAB, Aspen Plus, and FEMLAB. The interested reader may pursue the references for more specific details. 

Abramowitz, M. A., Stegan. I. A. (eds), Handbook of Mathematical Functions. National Bureau of Standards Gathessburg, MD, 1964. 

Aguilo, A., Penrod, J. D., Acetaldehyde. In Encyclopedia of Clu-mical Processing and Design. Vol. 1, McKetta, J. J. (ed.). Marcel Dekker New York, 1976. 

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