A New Approximation Method for Multi-Pantograph Type Delay Differential Equations Using Boubaker Polynomials

Yüzbaşl A., Çetin B.

International Journal of Computational Methods, cilt.21, sa.3, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s0219876223500342
  • Dergi Adı: International Journal of Computational Methods
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Boubaker polynomials, collocation method, collocation points, error estimation, Pantograph equation, pantograph-Type delay differential equations
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a new approaching technique is offered to unravel multi-pantograph-Type delay differential equations. The suggested new method is a collocation method based on integration and Boubaker polynomials. As the main idea of the method, the process starts by approaching the first derivative function in the equation in the form of truncated Boubaker series. Then this approximating form is composed in the matrix form. The unknown function is then obtained by integrating the approximate derivative function and expressing it as a matrix. Using the approximation, the matrix forms for the proportionally delayed terms in the equation are derived. In addition, operational matrix forms are constructed for convenience in the method. By using these matrix forms and matrix operations, the problem is reduced to a system of algebraic linear equations. The method is illustrated through numerical implementations and compared with existing techniques in the literature. The results demonstrate the effectiveness and reliability of the proposed approach, highlighting its superiority over other methods.