Operads, graphs, and perturbation series

1999 ◽  
pp. 175-200
Keyword(s):  
Perturbation Series

In what schemes can QCD perturbation series converge?

1984 ◽  
Vol 29 (12) ◽  
pp. 2884-2890 ◽  
Author(s):  
C. J. Maxwell
Keyword(s):  
Perturbation Series

On the convergence of the operator method perturbation series

1984 ◽  
Vol 104 (8) ◽  
pp. 401-404 ◽  
Author(s):  
Francisco M. Fernández ◽  
Alejandro M. Mesón ◽  
Eduardo A. Castro
Keyword(s):  
Operator Method ◽  
Perturbation Series

New Trends in Asymptotic Approaches: Summation and Interpolation Methods

2001 ◽  
Vol 54 (1) ◽  
pp. 69-92 ◽  
Author(s):  
Igor V. Andrianov ◽  
Jan Awrejcewicz
Keyword(s):  
Applied Sciences ◽  
Solid Mechanics ◽  
State Of The Art ◽  
Asymptotic Methods ◽  
Perturbation Series ◽  
Review Article ◽  
Point Of View ◽  
Advantages And Disadvantages ◽  
New Methods ◽  
Local Character

In this review article, we present in some detail new trends in application of asymptotic techniques to mechanical problems. First we consider the various methods which allows for the possibility of extending the perturbation series application space and hence omiting their local character. While applying the asymptotic methods very often the following situation appears: an existence of the asymptotics ε → 0 implies an existence of the asymptotics ε → ∞ (or, in a more general sense, ε → a and ε → b). Therefore, an idea of constructing a single solution valid for a whole interval of parameter ε changes is very attractive. In other words, we discuss a problem of asymptotically equivalent function constructions possessing for ε → a and ε → b a known asymptotic behavior. The defined problems are very important from the point of view of both theoretical and applied sciences. In this work, we review the state-of-the-art, by presenting the existing methods and by pointing out their advantages and disadvantages, as well as the fields of their applications. In addition, some new methods are also proposed. The methods are demonstrated on a wide variety of static and dynamic solid mechanics problems and some others involving fluid mechanics. This review article contains 340 references.

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

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