Research
My research interests are numerical and functional analysis. In particular, numerical approximations of evolution equations, partial differential equations, semigroups of operators, operational calculus, integral transforms, as well as finite difference and finite element methods.
Publications:
Peer-Reviewed Research Articles Published (or in Press):
- Rational inversion of the Laplace transform (with F. Neubrander and K. Ozer). J. Evol. Eq. (2012), In Press. DOI: 10.1007/s00028-012-0139-1.
- Rational approximation schemes for solutions of the first and second order Cauchy problem. Proc. Amer. Math. Soc. 137 (2009), 3885-3898. DOI: 10.1090/S0002-9939-09-09891-8.
- Rational approximation schemes for bi-continuous semigroups. J. Math. Anal. Appl. 344 (2008), no. 2, 956–968. DOI: 10.1016/j.jmaa.2008.02.068.
Research articles submitted for publication:
- Sharp numerical inversion of the Laplace transform.
Research Articles in Preparation:
- Approximation of semigroups generated by fractional powers of closed operators (with S. McAllister and K. Zito).
Other Publications:
- Rational Approximation Schemes for Solutions of Abstract Cauchy Problems and Evolution Equations. Ph.D. Dissertation. Louisiana State University (2008).
The current support of the National Science Foundation under Award 1008101 and Award 1238775 is greatly acknowledged.