An approximate solution of an equation of V. A. Ambartsumyan. (Russian. English summary) Zbl 0991.65144

Khudyaev, S. I.; Kojnova, L. V.

Vestn. Syktyvkar. Univ., Ser. 1, Mat. Mekh. Inform. 4, 195-206 (2001).

Summary: An algorithm for the numerical solution of the well-known Ambartsumyan equation is suggested (this eduation is widely used in astrophysics, the theory of transport of neutrons, etc.). Numerical calculations are carried out for the practically important case of Milne kernel. A correlation is given with an approximate solution obtained earlier. The role of the solution of the Ambartsumyan equation is shown by the concrete example of asymptotics for the solution of the Wiener-Hopf integral equation.

MSC:

65R20	Numerical methods for integral equations
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)

Keywords:

algorithm; Ambartsumyan equation; asymptotics; Wiener-Hopf integral equation