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 Calculus.
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 international conferences.
Membership of Professional Societies: Society of Computer Aided Engineering – Member National Union of Romanian Scientists (Founding member), Balkan Society of Geometers member.
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.