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Numerical Methods for Problems With Moving Fronts: Bruce A. Finlayson

I began this book while serving as the Gulf Professor of Chemical Engineering at Carnegie Mellon University - indeed, without that sabbatical the book could not have been written. The faculty there was very supportive of my efforts and the University provided important library and office facilities. My time there was too short to finish the book and it has been a slowly simmering project ever since.

The book was written on the Macintosh computer and many of the ideas developed while writing the book were possible because of the graphics programs which could be used to demonstrate the results. The equations - of which there are many - were written using the program Math Writer. This equation writing software is so easy to use that some of the algebra was done on the computer (substituting one equation into another, etc.). There are equations in the book that have never been written down by hand. Also, since equation writing was so simple, I tended to merely repeat an equation rather than refer back to an earlier chapter for it. Thus the reader can follow the ideas more easily. You will notice many graphs in the book; these were important in the testing of the ideas. Oftentimes an author in the literature will present a new method and present results from it, but there may be no comprehensive comparison with other methods. Thus I felt it important to try all methods on all problems, insofar as that is possible. The graphical display helps decide which methods to keep and which ones to discard. It is also possible to learn things graphically that are harder to learn otherwise. For example, the von Neumann analysis of stability can be tedious when done algebraically, so I show graphical results which present the same information. They are not merely graphical displays of the algebraic results, but are graphical presentations of the information contained in the algebraic results - without generation of the algebraic results. For example, if you want to see in what regions of the x-y plane a function f(x,y) is less than one, you usually set f=l and solve for x(y) or y(x). However, you can also plot f(x,y) and see where it is 1, and you can plot contours where f=l. These approaches are much faster and are necessary when dealing with dozens of methods, as I was. To learn the material in the book it is necessary that you exercise the computer programs provided. I have witnessed students learning things much faster by operating the computer program, chiefly because of its graphical output. To some extent the graphical display helps you use the left side of your brain - and this is ideally suited to a generation raised on TV!

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