Raising the Orders of Unconventional Schemes for
Ordinary Differential Equations

The PostScript file for the thesis, as a whole, is too large to download over the internet and also too large for most printers. It has to be broken into small pieces.

• All pages up to page 26 (gzip'ed, size 87 KB)
• Page 27 to Page 60 (gzip'ed, size 88 KB)
• Page 61 to Page 120 (gzip'ed, size 232 KB)
• Each of Pages 121 - 129 contains a figure that consumes lots of spaces, and thus takes time to downloan over the internet. If you are tired of waiting, please email me and I'll be glad to mail you hard copies of these pages and Page 155 below.
  • Page 121 (gzip'ed, size 1680 KB)
  • Page 122 (gzip'ed, size 1672 KB)
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  • Page 125 (gzip'ed, size 1680 KB)
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  • Page 129 (gzip'ed, size 512 KB)
• Page 130 to Page 154 (gzip'ed, size 77 KB)
• Page 155 (gzip'ed, size 144 KB)
• Page 156 to Page 190 (gzip'ed, size 94 KB)
• Appendexs A - F (Page 191 to Page 251) (gzip'ed, size 248 KB)

See also a short introductory paper: Composition constants for raising the orders of unconventional schemes for ordinary differential equations, by W. Kahan and R.-C. Li, Mathematics of Computation, vol. 66, pp.1089-1099, 1997.

A software package ( introduction and package) consisting of programs in a few different computer languages has been released to help people obtaining mechanically high order quality schemes that previously were obtained only very painfully, as well as their usage.

Comments and criticisms are appreciated.