Difference Potentials Method and its Applications to Composite Domains Problems and to Chemotaxis Models in Biology

Yekaterina Epshteyn
Department of Mathematics
University of Utah
Salt Lake City, Utah, USA


In this talk, we will give an introduction to the Difference Potentials Method (DPM). DPM was originally proposed by Viktor S. Ryaben'kii in 1969. DPM can be understood as the discrete version of the method of generalized CalderonĄ¯s potentials, and CalderonĄ¯s boundary equations with projections in the theory of partial differential equations. The DPM on its own, or in combination with other numerical methods, is an efficient tool for the solution of the interior and exterior boundary value problems in arbitrary irregular domains. We will discuss recently developed efficient numerical schemes based on the idea of Difference Potentials for elliptic and parabolic composite domains/interface problems, as well as for chemotaxis models in biology. Some numerical experiments to illustrate the accuracy and the robustness of the developed methods will be presented as well.