Combined Spectral and Finite Difference Methods for a
Stationary Neutron Transport Equation
Professor Olga Martin
Applied Sciences Faculty
University "Politehnica" of Bucharest
Splaiul Independentei 313
Abstract: The spectral method that we use in our
paper is closely related with the finite element method
(FEM). The main difference between them is that FEM
approximates the solution as a linear combination of
piecewise functions, which are nonzero on small
sub-domains, while a spectral method approximates the
solutions as linear combination of continuous functions
that are generally nonzero over the domain of solution.
Therefore, the finite element method is a local
approach, while the spectral method is a global approach
of the phenomenon. The approximate solution of our
boundary problem for an integral-differential equation
is a trigonometric series with variable coefficients.
The comparative study of this solution with the exact
solution for a numerical example leads to the
conclusions regarding the values of errors.
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 paperwork ‘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, Applied Sciences Faculty,
University Politehnica of Bucharest.
Fields of specialization: Mathematical Analysis,
Mathematical Physics, Computational and Experimental
Solid Mechanics, Numerical Analysis, Statistical
She has published over 80 research papers and 18 books.
Member of the editorial boards of 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
Membership of Professional Societies: Society of
Computer Aided Engineering – Member National Union of
Romanian Scientists (Founding member), Balkan Society of
Reviewer: WSEAS Press (books and journals), Scientific
Bulletin, Politehnica University of Bucharest
Scientific Evaluation Societies: RELANSIN, Politehnica
University of Bucharest, ARACIS, Bucharest, CNCSIS,
Bucharest, National Science Fund of Bulgaria.