NUMERICAL SOLUTION OF VOLTERRA SERIES WITH ERROR ESTIMATION

Tari A., Bildik N.

Applied and Computational Mathematics, vol.21, no.1, pp.3-20, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.30546/1683-6154.21.1.2022.3
  • Journal Name: Applied and Computational Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3-20
  • Keywords: Volterra Series, Multiple Non-linear Volterra Integral Equations, Differential Trans-form Method, Error Estimation, Convergence
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

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.