NUMERICAL SOLUTION OF VOLTERRA SERIES WITH ERROR ESTIMATION

Tari A., Bildik N.

Applied and Computational Mathematics, cilt.21, sa.1, ss.3-20, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.30546/1683-6154.21.1.2022.3
  • Dergi Adı: Applied and Computational Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3-20
  • Anahtar Kelimeler: Volterra Series, Multiple Non-linear Volterra Integral Equations, Differential Trans-form Method, Error Estimation, Convergence
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this paper, an important applied problem, namely Volterra series, is investigated. Here, the well-known differential transform (DT) method is extended to solve the multiple non-linear Volterra integral equations which lead to Volterra series. To this end, some basic properties of DT are given, then by proving some theorems, the DT method is extended to solve the mentioned equations. Next, a scheme to estimate the error of solution is proposed and the convergence of the method is proved. Finally, the validity and applicability of the proposed method is illustrated by some examples.