Timothy Lucas, Instructor

Timothy Lucas
Office Location:  029B Physics Bldg
Office Phone:  (919)-660-2828
Email Address: send me a message

Typical Courses Taught:

Office Hours:


PhD in MathematicsDuke University2006
M.A. in MathematicsDuke University2001
B.A. in MathematicsOccidental College2000

Applied Math
Research Interests: Numerical Analysis, Partial Differential Equations, Multigrid, Stochastic Differential Equations and Parallel Computing

I am studying a three-dimensional system of reaction-diffusion equations with stochastic source terms that arises from an immunology model. I have shown convergence of a first order splitting method for this system. This allows us to take advantage of known numerical methods for the diffusion, reaction and stochastic differential equations. In particular, I have implemented a parallel multigrid scheme for the diffusion.

I am currently working with Dr. William K. Allard in the Mathematics department and Dr. Thomas B. Kepler in the Center for Computational Immunology.


Numerical Analysis • Partial Differential Equations • Multigrid • Stochastic Differential Equations • Parallel Computing

Recent Publications

  1. T.A. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Submitted, Fall, 2007) (Submitted.)  [abs] [author's comments]
  2. F. Mitha, T.A. Lucas, F. Feng, T.B. Kepler and C. Chan, The multiscale systems immunology project: Software forcell-based immunological simulation, Source Code for Biology and Medicine (Submitted, Fall, 2007) (Submitted.)  [abs]
Selected Talks

  1. Numerical Methods for an Immunology Model Using, January 7, 2008, AMS Session on Applications of Mathematics, San Diego, CA    
  2. Numerical Solutions of an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms, November 8, 2007, Virginia Commonwealth University    
Selected Grant Support