Piecewise Jacobi–Picard Iteration Method for Solving Nonlinear Initial Value Problems on Large Domains

M. Tafakkori-Bafghi, G. B. Loghmani, M. Heydari, X. Bai

Research output: Contribution to journalArticlepeer-review


In this investigation, an effective numerical technique, called the piecewise Jacobi–Picard iteration (PJPI) method, to find the approximate solution of nonlinear initial value problems (IVPs) with high accuracy on large domains is proposed. This method is based on the Jacobi–Picard iteration method combined with the domain decomposition technique. To reduce the CPU time, a vector-matrix structure of the proposed method is designed. Based on this vector-matrix representation, the convergence analysis of the PJPI method is studied. Several applied problems in different fields of science and engineering such as physics and biology are presented to demonstrate the capability and efficiency of the PJPI method by comparing it with the fourth- and fifth-order Runge–Kutta–Fehlberg (RKF45) method and some other existing methods in the literature.

Original languageEnglish (US)
Pages (from-to)595-613
Number of pages19
JournalIranian Journal of Science and Technology, Transaction A: Science
Issue number2
StatePublished - Apr 2022

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Mathematics(all)
  • Agricultural and Biological Sciences(all)
  • Physics and Astronomy(all)
  • Earth and Planetary Sciences(all)


  • Initial value problems
  • Jacobi polynomials
  • Jacobi–Gauss quadrature
  • Picard iteration method
  • Piecewise Jacobi–Picard iteration
  • Vector-matrix structure


Dive into the research topics of 'Piecewise Jacobi–Picard Iteration Method for Solving Nonlinear Initial Value Problems on Large Domains'. Together they form a unique fingerprint.

Cite this