John Butcher's support page for

Numerical Methods for Ordinary Differential Equations 

Second edition,  ISBN: 978-0-470-72335-7

Publication date: March 2008


Judging this book by its cover

Thanks to a combination of mathematical imagery with graphical artistry, Wileys have created a most attractive cover for this second edition.  Even before the book was published, a colleague in a distant part of the world, said how much she liked it, just on the basis of the cover.   Underneath the words and the design features, there is a picture with a meaning.   The meaning concerns the (2,1) Padé approximation to the exponential function.  When this approximation is divided by the exponential function itself, the function of a complex variable which results is a link between the order of accuracy of a numerical method and its stability properties.  The lines shown in the diagram are contour lines for the real and imaginary parts of the logarithm of this function.  These are related in turn to order stars and order arrows.  To find out more, you will need to delve into the book itself.