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An estimator “over a run” for a solution of linear and nonlinear radiative transfer equations in the large. (English. Russian original) Zbl 0842.65097
Russ. Acad. Sci., Dokl., Math. 50, No. 1, 39-42 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 337, No. 2, 162-164 (1995).
Using a so-called estimator “over a run”, the Monte Carlo method is considered to solve the equation of radiative transfer under the conditions of plane symmetry of the form $v{\partial \Phi(z, \mu, v)\over \partial z}+ \sigma(z, v)\Phi(z, \mu, v)=\sigma_1(z, v) \int w(\mu', v'\to \mu,v;z)\Phi(z, \mu',v') d\mu' dv'+ \Phi_0(z, \mu, v),$ where $$\sigma_1$$ is the cross-section, $$w(\mu', v'\to \mu, v; z)$$ are the scattering indicatrices, $$\sigma(z, v)$$ is the total cross-section, $$\mu$$ is the direction cosine with axis $$z$$ and $$v$$ is the velocity of the particle. Optimal relations are derived for the estimator to minimize the labor $$S$$ in the iterative solution of the above problem.
Reviewer: V.Burjan (Praha)
##### MSC:
 65R20 Numerical methods for integral equations 65C05 Monte Carlo methods 85A25 Radiative transfer in astronomy and astrophysics 45K05 Integro-partial differential equations