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

Erdogan Madenci, Mehmet Dorduncu, Atila Barut, Michael Futch

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish (US)
JournalNumerical Methods for Partial Differential Equations
DOIs
StateAccepted/In press - 2017

Fingerprint

Linear partial differential equation
Nonlinear Partial Differential Equations
Partial differential equations
Mathematical operators
Differential operator
Numerical Solution
Explicit Methods
Implicit Method
Dirichlet
Discontinuity
Jump
Partial differential equation
Discretization
Boundary conditions
Singularity
Robustness
Derivatives
Derivative

Keywords

  • Differential
  • Equations
  • Nonlocal
  • Partial
  • Peridynamic

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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