On the solution of Fredholm-Volterra integral equation with discontinuous kernel in time.

Authors

  • Sameeha Ali Raad Umm AlQura University
  • M. A. Abdou Faculty of Education, Alexandria University.
  • M. M. El - Kojok College of Sciences and Arts, Qassim University

DOI:

https://doi.org/10.24297/jam.v9i4.2395

Keywords:

Linear system of Volterra integral equations (LSVIEs), Toeplitz matrix method (TMM), Linear algebraic system (LAS)

Abstract

The existence of a unique solution of Fredholm-Volterra integral equation (F-VIE) under certain conditions, are discussed and proved. The Fredholm integral term (FIT)  is considered in position with continuous kernel, while the Volterra integral term (VIT) in time with singular kernel. Using a numerical method, the F-VIE is transformed to a linear system of Volterra integral equations (LSVIEs). Then after using Toeplitz matrix method (TMM), we have a linear algebraic system (LAS). Finally, two applications are given, numerical results are obtained, and the error, in each case, is calculated.

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Author Biographies

Sameeha Ali Raad, Umm AlQura University

Mathematics

M. A. Abdou, Faculty of Education, Alexandria University.

Mathematics

M. M. El - Kojok, College of Sciences and Arts, Qassim University

Mathematics

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Published

2014-11-05

How to Cite

Raad, S. A., Abdou, M. A., & El - Kojok, M. M. (2014). On the solution of Fredholm-Volterra integral equation with discontinuous kernel in time. JOURNAL OF ADVANCES IN MATHEMATICS, 9(4), 2553–2563. https://doi.org/10.24297/jam.v9i4.2395

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