Abstract: The main problem in a reactor theory is to find the neutrons distribution, hence its density. This is the solution of an integral-differential equation named the neutron transport equation and its knowledge guaranties the safety and efficiently of the nuclear reactor. This study deals with a topical problem of the nuclear-physics: the solving of neutron transport equation with variable coefficients. We shall use the linearized version of the Boltzmann equation with the numerous applications in physics, geophysics, astrophysics, light scattering, radiative transfer of stellar and planetary atmosphere. To solve the transport equation we subdivide the overall domain into regions within which the coefficients of equation (i.e. the medium properties) are constant. A new homotopy perturbation method is applied to obtain the continuous solution of the integral-differential equation for a multipoint boundary value problem. The idea of this method consists in determining the series, whose sum represents this solution. The speed of convergence of the series is quite good, so only a few first terms calculation ensures the satisfactory approximation of the sought solution. A numerical example that confirms the usefulness of the proposed algorithm for solving the problems of this kind is also presented.

Brief Biography of the Speaker:
Olga Martin graduated the Faculty of Mathematics and Mechanics, University of Bucharest, Romania. She received his PhD in mathematics with the specialization in Dynamic Plasticity with paper work ‘Applications of the Finite Element Method in Dynamic Plasticity’. During of twenty years, she had been senior researcher in Aircraft Institute, Strength Materials Department. Technical experience: structural strength computing reports using ANSYS program (wing-fuselage, fuselage frame, fin, elevator, rudder and aileron), dynamic and static test-programs for aircraft structures, fatigue test-programs for aircraft structures, iterative methods for the study of the reactions, which correspond to movable control surfaces, attached at n – points to an elastic structure and program of this, static and fatigue computation of the propeller (mono-bloc hub, blades and blades retention system).
Nowadays, she is Professor at Applied Sciences Faculty, University “Politehnica” of Bucharest. Fields of specialization: Mathematical Analysis, Mathematical Physics, Computational and Experimental Solid Mechanics, Numerical Analysis, Statistical Calculus. She has published over 90 research papers and 18 books.
Member of the editorial boards: Politehnica Sci. Bull. Series A, WSEAS Transactions on Applied and Theoretical Mechanics, WSEAS Transactions on Mathematics and she was involved in the program/organizing committees for many international conferences.
Membership of Professional Societies: Society of Computer Aided Engineering – Member National Union of Romanian Scientists (Founding member), Balkan Society of Geometers member, Romanian Society of Mathematicians.
Reviewer: WSEAS Press (books and journals), Scientific Bulletin, University “Politehnica” of Bucharest, Acta Mathematica universitatis Comenianae, Journal of Quantitative Spectroscopy and Radiative Transfer. Scientific Evaluation Societies: RELANSIN, University “Politehnica” of Bucharest, ARACIS, Bucharest, Bucharest, National Science Fund of Bulgaria.