This paper describes a numerical procedure to solve the homogeneous boundary problem for a stationary transport equation. The stability and convergence of the proposed finite differences scheme is proved. The error value that corresponds to the numerical solution is also obtained using the Lax theorem.

The solution of a boundary value problem for an integral-differential equation is presented, using the method of decomposition for a transport equation in the stationary case and a plan-parallel geometry and an algorithm based on the variational form of the integral identity method. Several numerical examples are included.

Are approched the concepts of the abstract functional analysis that make possible the solution of the boundary problems for a Helmholtz equation and the integral-differential equations using Riesz's theorem, Lax-Milgram theorem and Hille-Yosida theorem. The direct methods for the solution of differences equations, the variational-differences technique: the method of finite elements,errors and stability studies and many technical applications are

In this paper is presented a variational method for approximating solutions of the Dirichlet problem for the neutron transport equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution with respect to the steps of two grids.

Using a splitting method for a stationary transport equation we obtain the solution with an algorithm based on the variational form of the integral identity method. Numerical results are presented to prove the accuracy and computational efficiency of the algotithm.

Existence and uniqueness of the solution of a non-stationary transport equation subject to the boundary and the initial conditions are proved via the Hille-Yosida theory.