A numerical technique for solving functional integro-differential equations having variable bounds

A numerical technique for solving functional integro-differential equations having variable bounds 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 burcu.gurbuz@uskudar.edu.tr Elçin Gökmen egokmen@mu.edu.tr Mehmet Sezer mehmet.sezer@cbu.edu.tr Department http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

A numerical technique for solving functional integro-differential equations having variable bounds

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-018-0653-z
Publisher site
See Article on Publisher Site

Abstract

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 burcu.gurbuz@uskudar.edu.tr Elçin Gökmen egokmen@mu.edu.tr Mehmet Sezer mehmet.sezer@cbu.edu.tr Department

Journal

Computational and Applied MathematicsSpringer Journals

Published: May 30, 2018

References

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