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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)
65R20 Numerical methods for integral equations
65C05 Monte Carlo methods
85A25 Radiative transfer in astronomy and astrophysics
45K05 Integro-partial differential equations