Date: February 6-10, 2014
Location: Texas A&M University,
College Station, Texas
Organizers: Meriem Laleg (KAUST)
Raytcho Lazarov (Texas A&M)
Bill Rundell (Texas A&M)

This four day workshop will concentrate on the mathematical aspects of fractional order partial differential equations and will have three focus areas:

  • Modeling. Anomolous diffusion in both space and time variables; applications; what we can assume and what needs to be determined. Specific applications will include waves in porous media, viscoelasticity, financial models, regularization methods for imaging.
  • Numerical analysis. Going beyond finite differences; overcoming the “curse of non-locality”; developing fast solvers with proven error bounds; multi-dimensional finite element methods.
  • Inverse problems. Some of the very basic inverse problems for fractional order equations have very different outcomes in regards to uniqueness and ill-posedness from their classical counterparts leading to very different physics for the model. We want to explore and understand these ideas further.

We plan 25 to 30 participants and seek an “Oberwolfach style” with a relatively low density of talks. We anticipate ten 45 minute lectures and several shorter presentations, but expect that some talks will be added as a consequence of workshop discussions.

Funding for this workshop is through the Texas A&M Institute for Applied Mathematics and Computational Science in co-operation with the King Abdullah University of Science and Technology.

 

Schedule

Friday, February 7, 2014
8:55 – 9:00 William Rundell Introduction
9:00 – 10:00 Jin Cheng The Mathematical Model for Pollution Problems and Related Inverse Problems (abstract)
10:00 – 11:00 Jan Hesthaven Spectral Methods for Fractional Differential Equations (abstract)
11:00 – 11:20

Coffee Break
11:20 – 12:00 Bilal Chanane Fractional Sturm-Liouville problems
12:00 – 13:30

Lunch
13:30 – 14:30 Wenting Chen Pricing Option derivatives under the fractional Black-Scholes model (abstract)
14:30 – 15:30 Kassem Mustapha Discontinuous Galerkin methods for fractional diffusion problems (abstract)
15:30 – 16:00

Coffee Break
16:00 – 16:30 Hong Wang Mathematical analysis and fast numerical methods for space-fractional diffusion equations (abstract)
16:30 – 17:00 Dongwoo Sheen Laplace transform method for fractional diffusion equations (abstract)
16:40 – 17:30 Group discussions Rooms 628 and 612 in Blocker

 

Saturday, February 8, 2014
9:00 – 10:00 Masahiro Yamamoto Inverse problems for fractional diffusion equations (abstract)
10:00 – 11:00 Meriem Laleg A novel method for parameter identification in fractional space advection diffusion equation (abstract)
11:00 – 11:20

Coffee Break
11:20 – 12:00 Dumitru Baleanu New trends in fractional calculus and its application (abstract)
12:00 – 13:30

Lunch
13:30 – 14:30 Xiang Xu Local stability for an inverse coefficient problem of a fractional diffusion equation (abstract)
15:15 – 15:45

Coffee Break
15:45 – 16:15 Zhi Zhou Finite element method for fractional diffusion equations (abstract)
16:15 – 16:45 Lihua Zuo Theta-function method for time-fractional reaction-diffusion equation (abstract)
16:45 – 17:15 Abeer Aldoghaither Direct and Inverse Source Problem for a Space Fractional Advection Dispersion Equation (abstract)
17:15 – 18:00 Group discussions Rooms 628 and 612 in Blocker

 

Sunday, February 9, 2014
9:00 – 10:00 John Barrick TBA
10:00 – 11:00 Joe Pasciak Numerical Approximation of Fractional Powers of Elliptic Operators (abstract)
11:00 – 11:20

Coffee Break
11:20 – 12:00 Feng Chen TBA
12:00 – 13:30

Lunch
13:30 – 16:30 Group discussions Rooms 628 and 612 in Blocker