African Journal of Mathematics and Computer Science Research
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Article Number - D31A03660981


Vol.9(3), pp. 15-23 , September 2016
DOI: 10.5897/AJMCSR2016.0660
ISSN: 2006-9731



Full Length Research Paper

Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution



R. T. Matoog
  • R. T. Matoog
  • Faculty of Applied Science, Umm Al– Qurah University, Makah, Kingdom of Saudi Arabia.
  • Google Scholar







 Received: 07 August 2016  Accepted: 20 September 2016  Published: 30 September 2016

Copyright © 2016 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0


In this paper, we prove the existence of at least one solution for Volterra- Hammerstein integral equation (V-HIE) of the second kind, under certain conditions, in the space , Ω is the domain of integration and T is the time. The kernel of Hammerstein integral term has a singularity, while the kernel of Volterra is continuous in time. Using a quadratic numerical method with respect to time, we have a system of Hammerstein integral equations (SHIEs) in position. The existence of at least one solution for the SHIEs is considered and discussed. Moreover, using Toeplitz matrix method (TMM), the SHIEs are transformed into a nonlinear algebraic system (NAS). Many theorems related to the existence of at least one solution for this system are proved. Finally, numerical results and the estimate error of it are calculated and computed using Mable 12.

 

Key words: Volterra- Hammerstein integral equation, nonlinear algebraic system (NAS), singular kernel, Toeplitz matrix method, Hölder inequality.

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APA Matoog, R. T. (2016). Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution. African Journal of Mathematics and Computer Science Research, 9(3), 15-23.
Chicago R. T. Matoog. "Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution." African Journal of Mathematics and Computer Science Research 9, no. 3 (2016): 15-23.
MLA R. T. Matoog. "Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution." African Journal of Mathematics and Computer Science Research 9.3 (2016): 15-23.
   
DOI 10.5897/AJMCSR2016.0660
URL http://academicjournals.org/journal/AJMCSR/article-abstract/D31A03660981

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