Perturbation-iteration method applied to partial differential equations

Pakdemirli M.

Journal of Interdisciplinary Mathematics, vol.28, no.2, pp.425-439, 2025 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.47974/jim-1744
  • Journal Name: Journal of Interdisciplinary Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.425-439
  • Keywords: Perturbation techniques, Iteration algorithms, Partial differential equations, Approximate solutions
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Partial differential equations are treated with the Perturbation Iteration Method (PIM) Sample equations possessing exact analytical solutions were treated for comparison with the iteration solutions. Two different iteration algorithms are applied to the differential equations. Linear as well as nonlinear problems are treated. Exact solutions are contrasted with the approximate solutions for each sample problem. It is shown that the Perturbation Iteration Method can be successfully applied to partial differential equations in construction of admissible approximate analytical solutions.