Complex Exponential Method for Solving Partial Differential Equations

Pakdemirli M.

Engineering Transactions, vol.72, no.4, pp.461-474, 2024 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.24423/engtrans.3334.2024
  • Journal Name: Engineering Transactions
  • Journal Indexes: Scopus, Applied Science & Technology Source, Compendex, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.461-474
  • Keywords: complex functions, partial differential equations, heat transfer, wave motion, beam vibrations
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

For constant-coefficient linear partial differential equations solvable by separation of variables, an alternative solution method is proposed. The method employs complex exponential functions to find exact analytical solutions. Examples include the heat conduction equation, homogenous and non-homogenous wave equations, and the beam vibration equation. The method can be effectively used for partial differential equations (PDEs) whose solutions can be expressed as a product of harmonic and/or exponential type series.