Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0653-z A numerical technique for solving functional integro-differential equations having variable bounds 1 2 3 Elçin Gökmen · 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. B Burcu Gürbüz email@example.com Elçin Gökmen firstname.lastname@example.org Mehmet Sezer email@example.com Department
Computational and Applied Mathematics – Springer Journals
Published: May 30, 2018
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