[This is a copy of the original document!]
 Institute of Physics Publishing Home Up Map Feedback
 Online Services Journals Magazines Books & Reference Inside Physics The Institute

 Search All Search Journal Search Issue

 Main Menu This Journal ToC Return to Abstract Filing Cabinet Help

[Previous Article] [Next Article]


J. Phys. A: Math. Gen. 31 No 18 (8 May 1998) 4301-4317
PII: S0305-4470(98)87859-1

Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators

Alexei V Sergeev and David Z Goodson
Department of Chemistry, Southern Methodist University, Dallas, TX 75275, USA

Received 26 September 1997, in final form 26 January 1998

Abstract. The divergent Rayleigh-Schrödinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Padé approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree. Different branches of the approximants converge to different branches of the function. The success of the high-degree approximants is attributed to their ability to model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter. An efficient recursive algorithm for computing the diagonal approximant sequence is presented.


Article Options:

[ PDF ] Acrobat PDF (630KB)
[ Hypercite ] References - including HyperCiteTM links
[ Postscript ] Gzipped PostScript (600KB)

Setup Information is available for Adobe Acrobat and Gzip compressed PostScript.


 Search All Search Journal Search Issue
 Main Menu This Journal ToC Return to Abstract Filing Cabinet Help
Electronic Journals v2.02. Copyright IOP Publishing Ltd 1995, 1996, 1997, 1998.

Сайт создан в системе uCoz