scholarly journals Hidden positivity and a new approach to numerical computation of Hausdorff dimension: higher order methods

2021 ◽  
Author(s):  
Richard S. Falk ◽  
Roger D. Nussbaum
Keyword(s):  
Hausdorff Dimension ◽  
Numerical Computation ◽  
Higher Order ◽  
New Approach ◽  
Higher Order Methods

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

A Comparison of Higher-Order Methods on a Set of Canonical Aerodynamics Applications

2011 ◽  
Author(s):  
Julie Andren ◽  
Haiyang Gao ◽  
Masayuki Yano ◽  
David Darmofal ◽  
Carl Ollivier Gooch ◽  
...  
Keyword(s):  
Higher Order ◽  
Higher Order Methods

New higher-order methods for the simultaneous inclusion of polynomial zeros

2011 ◽  
Vol 58 (2) ◽  
pp. 179-201 ◽  
Author(s):  
Miodrag S. Petković ◽  
Mimica R. Milošević ◽  
Dušan M. Milošević
Keyword(s):  
Higher Order ◽  
Polynomial Zeros ◽  
Higher Order Methods
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