Numerical-analytical algorithm to solve the equation of particle transport in plane geometry

We describe a numerical-analytical algorithm to solve the boundary-value problem for the integrodifferential equation of particle transport in a plane homogeneous medium. The general scheme of approximate solution of this problem is based on its reduction to the solution of some integral equation by summator operators of function approximation theory. Solvability conditions are established for the approximate equations and the algorithm errors are estimated. Working formulas are presented for the algorithm implemented in the form of a computer program. The summator operators in this algorithm are the algebraic interpolation operators with nodes at the extremal points of Chebyshev polynomials of first kind.