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Research Interests:
- Numerical solutions of partial differential
equations
- Computational mathematics
- Finite element method
- Inverse problems in optical tomographic imaging of
brain, and groundwater hydrology
- Mathematical biology (Avian influenza and spatial
epidemic models)
Publications:
- Necibe Tuncer, “Finite element method on arbitrary
surfaces,”submitted.
- Alexandra Smirnova, Necibe Tuncer, “Inverse problem
of groundwater hydrology by preconditioned iteratively regularized
Gauss-Newton method,” submitted.
- Necibe Tuncer, Maia Martcheva, “Analytical and
numerical approaches to coexistence of strains in a two strain SIS
model with diffusion,” submitted.
- A.J. Meir, Necibe Tuncer, “Radially projected finite
elements,” SIAM Journal of Scientific Computing, Vol.31, No.3, (2009).
- A.B. Bakushinsky, A.B. Smirnova and N. Tuncer,
“Relative computational efficiency of iteratively regularized methods.”
Journal of Inverse and Ill-posed Problems. 16, N7, 681694 (2008).
- N. Tuncer, “A novel finite element discretization of
domains with spheroidal geometry,” Ph.D.
Dissertation, Auburn University Library, (2007).
- S. Somali and N. Tuncer, “Shooting method and
extrapolation for singular two-point boundary value problems,”
International Journal of Computational and Numerical Analysis and
Applications, (2004), 1-11.
- H. Oruc, and N. Tuncer, “On the convergence and
iterates of q-Bernstein polynomials,” Journal of Approximation Theory,
117 (2002), 301-313.
- H. Oruc and N. Tuncer, “On the q-Bernstein
polynomials,” Proceedings of Algorithms for Approximations IV,
University Huddersfield Press, (2002), 52-59.
- A. B. Smirnova and N. Tuncer, Book chapter,
“Iteratively
Regularized Methods for Inverse Problem in Optical Tomography”
Introduction to Iterative Methods for Ill-Posed Problems, Gruyter,
Germany, (2010).
Work
in Progress:
- Necibe Tuncer, A.J. Meir, Anotida Madzwamuse,
“Radially projected finite elements for reaction diffusion systems on
arbitrary surfaces,” near completion for submission.
- Necibe Tuncer, A.J. Meir, Anotida Madzwamuse,
“Finite element method for pattern formation on evolving surfaces,”
near completion for submission.
- Necibe Tuncer, Yun Mei Chen, “Inverse problem for a
PET scan imaging.”
- Necibe Tuncer, Maia Martcheva, Patrick De Leenheer,
“A two strain SIS
model with equal diffusion coefficients.”
- Maia Martcheva, Necibe Tuncer, “Comparison of avian
influenza models by their fit to human influenza cases.”
NSF
Grants:
- Maia Martcheva (PI), Necibe Tuncer (CO-PI), Avian
Flu:
Modeling and implications for control, to be submitted, January 2011.
- Alexandra Smirnova (PI), Necibe Tuncer (CO-PI),
Advanced
computational methods in optical tomographic images, (declined), 2008.
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