A Galerkin-Like Approach to Solve Multi-Pantograph Type Delay Differential Equations

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YÜZBAŞI Ş., KARAÇAYIR M.

FILOMAT, cilt.32, sa.2, ss.409-422, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2298/fil1802409y
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.409-422
  • Anahtar Kelimeler: Delay differential equations, pantograph equation, Galerkin method, residual error correction, APPROXIMATION, ORDER, MODEL
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a Galerkin-like approach is presented to numerically solve multi-pantograph type delay differential equations. The method includes taking inner product of a set of monomials with a vector obtained from the equation under consideration. The resulting linear system is then solved, yielding a polynomial as the approximate solution. We also provide an error analysis and discuss the technique of residual correction, which aims to increase the accuracy of the approximate solution. Lastly, the method, error analysis and the residual correction technique are illustrated with several examples. The results are also compared with numerous existing methods from the literature.