THE NUMERICAL SOLUTION OF ONE GLASS OF NONLINEAR INTEGRAL EQUATIONS OF DISPERSED TYPE (VURKHU CHISLENOTO RESHENIE NA EDNA KLASA NELINEINI INTEGRALNI URAVNENIYA OT DISPERSONEN TIP)
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSONAFB OH
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The shortcomings of the ND method and of the Chew-Low-Salzman method for the numerical solution of singular nonlinear integral equations of the Low type, utilizing the preliminary regularization of those equations, are analyzed. The method is presented for the direct numerical solution without preliminary regularization of one particular class of Low type integral equations--the Chew-Low equation, which describes the P-wave resulting from the pion-nucleon interaction under the assumption that the nucleon is fixed. By utilizing certain substitutions of variables, the Chew-Low equation is transformed to a form for which solutions are derived by the method of successive approximations. Measures for eliminating the instability from the iterative process are indicated. The authors explain how the proposed method can be used to obtain adiabatic and resonance solutions of the Chew-Low equation. It is shown that the adiabatic solution ceases to be analytic when the coupling constant f squared 0.07. Some numerical results obtained by authors at the Computing Center of the Joint Institute of Nuclear Research at Dubna are presented.
- Numerical Mathematics
- Nuclear Physics and Elementary Particle Physics