Peridynamic differential operator for numerical analysis

Erdogan Madenci, Atila Barut, Mehmet Dorduncu

Research output: Book/ReportBook

164 Scopus citations


Introduction This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization. Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.

Original languageEnglish (US)
PublisherSpringer International Publishing
Number of pages282
ISBN (Electronic)9783030026479
ISBN (Print)9783030026462
StatePublished - Jan 1 2019


  • Coupled multi-field equations
  • Data
  • Differential equations
  • Differentiation
  • Discrete
  • Integral equations
  • Integro-differential equations
  • Multi-field equations
  • Nonlinear
  • Nonlocal
  • Ordinary
  • Partial
  • Peridynamic
  • Peridynamic least square minimization
  • Recovery
  • Transient
  • Transient implicit
  • Weak form of peridynamics

ASJC Scopus subject areas

  • General Engineering
  • General Materials Science
  • General Computer Science


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