Abstract: The integral-differential equations describe many physical phenomena in different fields of the science and nuclear engineering. The resolution of these equations is the subject of several papers in which the authors have approached in most cases numerical methods: the finite element method, Monte Carlo, truncated series of Chebyshev polynomials, the fictitious domain method, SN method.
In this paper we present an algorithm based on the homotopy perturbation method (HPM) to solve the homogeneous boundary value for a transport equation, whose solution is the density of particles. The homotopy perturbation method is a coupling of traditional perturbation method and the homotopy function in topology that continuously deforms the given problem to another, which can be easily solved. It uses an embedding parameter p as a “small parameter”, a power series in p and finally, using the techniques of HPM, the solution of the given problem will be the sum of a series.
The new version of He’s homotopy method upon which our algorithm is built yields rapid convergence of the solution series and usually only a few iterations lead to high accuracy solutions. A numerical example proves the validity and the great potential of this new homotopy method for particle transport problems.

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.