Computational modeling of the Balitsky–Kovchegov equation and its numerical solution using hybrid B-spline collocation technique

The dynamics of high-energy scattering of hadrons are governed by Quantum Chromodynamics (QCD). In the parton model of QCD, scattering can be represented as a kind of reaction–diffusion process and consequently can be included in the category of the Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equat...

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Published in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2022-06, Vol.5, p.100348, Article 100348
Main Authors: Thottoli, Shafeeq Rahman, Tamsir, Mohammad, Dhiman, Neeraj, Souadi, Galib
Format: Article
Language:English
Subjects:
Balitsky–Kovchegov equation
Collocation technique
HB-spline basis functions
Rubin–Graves type linearization technique
Stability analysis
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Summary:The dynamics of high-energy scattering of hadrons are governed by Quantum Chromodynamics (QCD). In the parton model of QCD, scattering can be represented as a kind of reaction–diffusion process and consequently can be included in the category of the Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equation. We perform a numerical study in the mean-field approximation of QCD evolution given by the Balitsky–Kovchegov (BK) equation, using the hybrid B-spline (HB-spline) collocation technique. The Rubin–Graves type linearization process is used to linearize the nonlinear terms. The accuracy and efficiency of the method are checked by taking numerical examples. It is noticed that the present method gives more accurate results than existing methods. The von Neumann stability analysis is also discussed for the discretized system of the BK equation.
ISSN:2666-8181
2666-8181
DOI:10.1016/j.padiff.2022.100348