Abstract
The iterative schemes based on the Continuous analogue of the Newton's method (CANM) have been applied to the solving a number of the QCD problems.
A mathematical statement of boundary problems is formulated for the QCD-inspired potential quarkonium model on the basis of Schwinger-Dyson and Bethe-Salpeter equations. The explicit form of these equations depends on a chosen effective potential. In the different cases we have the systems of nonlinear integral, integrodifferential or differential equations. The cases of the oscillator, Yukawa, Gauss, Coulomb and linear potentials are considered.
Authors are grateful to Russian Foundation for Basic Research RFBR (Grant 94-01-01119) for support.
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References
Kalinovsky Yu.L., Kallies W., Kaschluhn L., Münchow L., Pervushin V.N. and Sarikov N.A.: Mesons in the Low — Energy Limit of QCD. Fortschr. Phys. 38 (1990) 333–343
Puzynin I.V. and Zhanlav T.: On convergency of iteration on the basis of Continuous analogue of Newton method. Comput. Math.and Math.Phys. 32 (1992) 846–856
Amirkhanov I.V., Zemlyanaya E.V., Pervushin V.N., Puzynin I.V., Puzynina T.P., Sarikov N.A. and Strizh T.A.: Numerical investigation of Schwinger-Dyson and Bethe-Salpeter equations with Gauss and oscillator potentials at the framework of the quarkonium model. JINR Communication E11-94-509 (1994) 1–20
Amirkhanov I.V., Davlatov H.F., Zemlyanaya E.V., Pervushin V.N., Puzynin I.V., Puzynina T.P., Sarikov N.A. and Strizh T.A.: Numerical investigation of modification of QCD-inspired quarkonium model with the Yukawa potential. JINR Communication P11-94-523 (1994) 1–12
Amirkhanov I.V., Zemlyanaya E.V., Pervushin V.N., Puzynin I.V., Puzynina T.P., Sarikov N.A. and Strizh T.A.: Numerical investigation of Schwinger-Dyson and Bethe-Salpeter equations with Gauss potential at the framework of the quarkonium model. Math. Model. 6 (1994) 55–70
Amirkhanov I.V., Zemlyanaya E.V., Puzynin I.V., Puzynina T.P. and Strizh T.A.: On some problems of numerical investigation of the quarkonium model with the coulomb and linear potentials, Math. Model. 7 (1995) 34–48
Amirkhanov I.V., Zemlyanaya E.V., Pervushin V.N., Puzynin I.V., Puzynina T.P.and Strizh T.A.: Numerical analyzes of a quarkonium model at finite temperature. Math. Model. 8 (1996) (to appear)
Puzynin I.V., I.V.Amirkhanov I.V., Puzynina T.P. and Zemlyanay E.V.: The newtonian iterative scheme with simultaneous calculating the inverse operator for the derivative of nonlinear function. JINR Rapid Comm. 5[62]-93 (1993) 63–73
Ortega J.M. and Rheinboldt W.C.: Iterative solution of nonlinear equations in several variables. Academic Press (1970) N.Y.
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© 1997 Springer-Verlag Berlin Heidelberg
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Amirkhanov, I.V., Puzynin, I.V., Puzynina, T.P., Strizh, T.A., Zemlyanaya, E.V. (1997). CANM in numerical investigation of QCD problems. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_73
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DOI: https://doi.org/10.1007/3-540-62598-4_73
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