Professor B. A. Wade
wade@uwm.edu
www.uwm.edu/~wade
414.229.5225
I have been working on the development of high order accurate numerical algorithms for reaction-diffusion equations (parabolic partial differential equations) when the problem data is not regular. This research focuses on both theory and applications, for example, in chemotaxis, tumor modeling, and financial mathematics. These problems are challenging, where existing proofs leave out a lot of applications and are not usually sharp and
the nonlinear case is currently in need of much more investigation. The problems are especially challenging under conditions of
low regularity of the data and in models with high dimension.
I work on problems in computational stochastics with my colleague R. Stockbridge. At this time the focus is on stochastic control and
development of effective computational algorithms.
On a continuing basis I become involved with problems of industrial & interdisciplinary mathematics for various corporations or academic departments and institutes. The essential thing is to approach the problem without a preconceived idea of mathematical techniques. These activities require special attention to analysis and communication approaches appropriate for engineers and scientists, whose experiences and working styles differ significantly from those of a the academic mathematician.
Together with Professor Jesus Vigo-Aguiar of the Universidad de Salamanca, Spain, we are continually working to promote interdisciplinary research work in computational and mathematical analysis for diverse areas of science and engineering. To this end, we are co-organizers of a series of conferences (CMMSE) and are currently working on the development of a professional society of the same name.
"Stochastic Methods for Dirichlet Problems,"
Journal of Mathematical
Modeling and Algorithms (JMMA), (Online) DOI:
10.1007/s10852-005-9007-0, Volume 4, Number 3, November 2005
Pages: 317 - 330.
"Smoothing with Positivity-Preserving Pade
Schemes for Parabolic Problems with Nonsmooth Data, Numerical Methods for Partial
Differential Equations (NMPDE), Wiley Interscience, V. 21, No. 3, 2005,
pp. 553--573, DOI 10.1002/num. 20039.
"Stability of Phase-Based Gain Modulation with
Designer-Chosen Switch Functions," International Journal of Robotics
Research, V. 25, No. 8, August, 2006, pp. 781--796.
"High Order Smoothing Schemes for Inhomogeneous Parabolic Problems with
Applications to Nonsmooth Payoff in Option Pricing" Numerical Methods for Partial Differential Equations (NMPDE) V. 23(5),
2007, 1249--1276.
"Adapted BDF Algorithms Applied to Parabolic
Problems," Numerical Methods for Partial Differential Equations (NMPDE), V. 23, No. 2, pp.
350-365, 2007.
"On Smoothing of the Crank-Nicolson Scheme and Higher order Schemes
for Pricing Barrier Options" Journal of
Computational and Applied Mathematics (JCAM), V. 204, No. 1, July, 2007, pp.
144-158. Doi:10.1016/j.cam.2006.04.034.
"Stability of Phase-Based Gain Modulation with
Designer-Chosen Switch Functions," International Journal of Robotics
Research, V. 25, No. 8, August, 2006, pp. 781--796.
Numerical Solution of a Long-term Average Control Problem
for Singular Stochastic Processes," Mathematical Methods of Operations Research (Math Meth Oper Res), V. 66, 2007, 451--473.
"Smoothing Schemes for Reaction-Diffusion Systems with Nonsmooth Data,"
J. Computational & Applied Mathematics (JCAM), to appear in print, 2008. DOI 10.1016/j.cam.2008.01.017.