ABSTRACT: Lattice equations are used to model physical processes or to approximate solutions for continuous models. Various techniques, including Fourier transforms, Jacobi operator theory, and backward error analysis, provide means to construct and study the behavior of traveling-wave-like solutions for discrete reaction-diffusion equations and discrete semi-linear wave equations. The results supply waves speed estimates and necessary and sufficient conditions for fronts and pulses to fail to propagate due to inhomogeneities in the medium, as well as confirmation that certain discretizations reproduce the qualitative solution behavior of the corresponding partial differential equations.

BIO: After completing an M.S. degree in mathematical and computer sciences at Colorado School of Mines, Brian Moore earned his Ph.D. in mathematics at the University of Surrey in the United Kingdom in 2003. He held a postdoctoral research position at McGill University in Quebec, followed by a visiting assistant professorship at the University of Iowa. He is currently an Associate Professor of Mathematics at the University of Central Florida. His research interests are in numerical analysis and differential equations with emphasis on structure-preserving algorithms and lattice equations. His work has contributed to several scientific applications in neuroscience, material science, wave mechanics, and computer vision.