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New LevinIntegrate package for highly oscillatory integration

• To: mathgroup at smc.vnet.net
• Subject: [mg82055] New LevinIntegrate package for highly oscillatory integration
• From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
• Date: Wed, 10 Oct 2007 04:34:16 -0400 (EDT)

Hi all,

My LevinIntegrate package, for numerical integration of highly oscillatory
functions, is now available at
http://andrew.j.moylan.googlepages.com/levinintegrate.

LevinIntegrate is an automatic integrator based on Levin's method for highly
oscillatory integration. It outperforms NIntegrate (and other automatic
integrators) for a variety of irregularly oscillatory functions:

LevinIntegrate[Exp[I*Cosh[x]], {x, 0, 10}] // Timing
>> {0.02, -0.138718 + 1.20194 * I}

Compare with:

NIntegrate[Exp[I*Cosh[x]], {x, 0, 10}, MaxRecursion -> 50] // Timing
>> (warnings)
>> {4.546, -0.138718 + 1.20194 * I}

For more information or to download the package, see
http://andrew.j.moylan.googlepages.com/levinintegrate.

This is an early release of LevinIntegrate; it is still under development.
If you have any comments, suggestions, or problems, please do let me know of
them!

Andrew Moylan