Department of Mathematics

Applied Mathematics

  •  Novel nonlocal operators in arbitrary dimension enforcing local boundary conditions
  •  10/27/2017
  •  4:10 PM - 5:00 PM
  •  C100 Wells Hall
  •  Prof. Fatih Celiker, Department of Mathematics, Wayne State University

Abstract: We present novel nonlocal governing operators in 2D/3D for wave propagation and diffusion that enforce local boundary conditions (BC). The main ingredients are periodic, antiperiodic, and mixed extensions of kernel functions together with even and odd parts of bivariate functions. We present all possible 36 different types of BC in 2D which include pure and mixed combinations of Neumann, Dirichlet, periodic, and antiperiodic BC. Our construction is systematic and easy to follow. We provide numerical experiments that validate our theoretical findings. We also compare the solutions of the classical wave and heat equations to their nonlocal counterparts.

 

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science