Comp. Appl. Math.
A numerical technique for solving functional
integro-differential equations having variable bounds
· Burcu Gürbüz
· Mehmet Sezer
Received: 26 December 2017 / Revised: 11 May 2018 / Accepted: 19 May 2018
© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018
Abstract In this paper, a collocation method based on Taylor polynomials is presented to
solve the functional delay integro-differential equations with variable bounds. Using this
method, we transform the functional equations to a system of linear algebraic equations.
Thus, the unknown coefﬁcients of the approximate solution are determined by solving this
system. An error analysis technique based on residual function is developed to improve
the numerical solution. Some numerical examples are given to illustrate the accuracy and
applicability of the method. Finally, the data are examined according to the residual error
estimation. All numerical computations have been performed on the computer programs.
Keywords Functional integro-differential equations · Taylor polynomials · Collocation
points · Approximate solutions · Residual error technique
Mathematics Subject Classiﬁcation 45J05
PACS 41A58 · 65L60 · 41A55 · 65G99
Communicated by Antonio José Silva Neto.
Department of Mathematics, Faculty of Science, Mu˘gla Sıtkı Koçman University, Mu˘gla, Turkey
Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Üsküdar
University, Istanbul, Turkey
Department of Mathematics, Faculty of Science and Art, Celal Bayar University, Manisa, Turkey