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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1002/num.22167
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1726-1753
  • Keywords: peridynamic, nonlocal, partial, differential, equations
  • Erciyes University Affiliated: No

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