Numerical Methods for a Diffusive Class of Nonlocal Operators. Dr. Gabriela Jaramillo скачать в хорошем качестве

Numerical Methods for a Diffusive Class of Nonlocal Operators. Dr. Gabriela Jaramillo

Title: Numerical Methods for a Diffusive Class of Nonlocal Operators Speaker: Gabriela Jaramillo, University of Houston, gabriela@math.uh.edu Abstract: We develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $
u$, of diffusive type. In particular, we assume $
u$ is symmetric and exponentially decaying at infinity. We consider problems posed in bounded domains and in $\R$. In the case of bounded domains with nonlocal Dirichlet boundary conditions, we show the convergence of the scheme for kernels that have positive tails, but that can take on negative values. When the equations are posed on all of $\R$, we show that our scheme converges for nonnegative kernels. Since nonlocal Neumann boundary conditions lead to an equivalent formulation as in the unbounded case, we show that these last results also apply to the Neumann problem. Joint work with Loic Cappanera and Cory Ward. Programming language: Matlab. Repo: https://github.com/gabyjaramillo/Diff... For more information, please visit https://sites.google.com/view/onenonl...