Method of cumulative factorization used to solve a system of linear differential equations of the second order with transition conditions approximately

Certain physical problems lead to the solution of a system of linear differential equations of the second order with piecewise constant coefficients and prescribed transition conditions at certain points of the interval considered. The formulation of the problem and a description of the method of cumulative factorization, modified with respect to the problem with transition conditions is given. As compared with other approximate methods of solution, the requirements on the storage capacity of the computer are minimal. A problem of this type was generated in solving a system of multi-group diffusion equations in the theory of nuclear reactors. A simple numerical example is given. (author)