Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator


Madenci E., Dorduncu M. , Barut A., Futch M.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.33, no.5, pp.1726-1753, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1002/num.22167
  • Title of Journal : NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Page Numbers: pp.1726-1753
  • Keywords: peridynamic, nonlocal, partial, differential, equations

Abstract

This study presents numerical solutions to linear and nonlinear Partial Differential Equations (PDEs) by using the peridynamic differential operator. The solution process involves neither a derivative reduction process nor a special treatment to remove a jump discontinuity or a singularity. The peridynamic discretization can be both in time and space. The accuracy and robustness of this differential operator is demonstrated by considering challenging linear, nonlinear, and coupled PDEs subjected to Dirichlet and Neumann-type boundary conditions. Their numerical solutions are achieved using either implicit or explicit methods. (c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1726-1753, 2017