Integral Representation Method

1990 ◽  
pp. 218-254
Author(s):  
V. L. Girko
Keyword(s):  
Integral Representation ◽  
Representation Method

Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method

2017 ◽  
Vol 14 (01) ◽  
pp. 1750028 ◽  
Author(s):  
Gantulga Tsedendorj ◽  
Hiroshi Isshiki
Keyword(s):  
Diffusion Equation ◽  
Integral Representation ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Infinite Domain ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Representation Method ◽  
Advective Diffusion

Generalized integral representation method (GIRM) is designed to numerically solve initial and boundary value problems for differential equations. In this work, we develop numerical schemes based on 1- and 2-step GIRMs for evaluation of the two-dimensional problem of advective diffusion in an infinite domain. Accurate approximate solutions are obtained in both cases of GIRM and compared to the exact ones. The derivation of GIRM is straightforward and implementation is simple.

scholarly journals Some Properties of Generalized Gegenbauer Matrix Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ghazala Yasmin
Keyword(s):  
Integral Representation ◽  
Recurrence Relations ◽  
Matrix Polynomials ◽  
Hermite Matrix ◽  
Representation Method ◽  
Generating Matrix

Various new generalized forms of the Gegenbauer matrix polynomials are introduced using the integral representation method, which allows us to express them in terms of Hermite matrix polynomials. Certain properties for these new generalized Gegenbauer matrix polynomials such as recurrence relations and expansion in terms of Hermite matrix polynomials are derived. Further, several families of bilinear and bilateral generating matrix relations for these polynomials are established and their applications are presented.

scholarly journals The Valuation of Executive Stock Option Using the Integral Representation Method

2020 ◽  
Vol 10 (03) ◽  
pp. 431-447
Author(s):  
Yi-Long Hsiao ◽  
Li-Ling Chen ◽  
Chien-Jung Ting
Keyword(s):  
Integral Representation ◽  
Stock Option ◽  
Executive Stock Option ◽  
Representation Method

scholarly journals Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Cédric Mezrag ◽  
Giovanni Salmè
Keyword(s):  
Integral Representation ◽  
Minkowski Space ◽  
Integral Equations ◽  
Vector Boson ◽  
Coupled System ◽  
The Self ◽  
Consistency Check ◽  
System Of Integral Equations ◽  
Perturbative Regime ◽  
Representation Method

AbstractThe approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- and Bethe-Salpeter equations, in Minkowski space. The achieved result, namely a 6-channel coupled system of integral equations, eventually allows one to determine the three Källén–Lehman weights for fully dressing the propagators of fermion and photon. A first consistency check is also provided. The presented formal elaboration points to embed the characteristics of the non-perturbative regime at a more fundamental level. It yields a viable tool in Minkowski space for the phenomenological investigation of strongly interacting theories, within a QFT framework where the dynamical ingredients are made transparent and under control.

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