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Ass. Lect. Mohamed Abdallah Abdel-Aty Ali :: Publications:

A study of normality and continuity for mixed integral equations
Authors: M. A. Abdou; M. E. Nasr; M. A. Abdel-Aty
Year: 2018
Keywords: Mixed integral equations; A linear system of Fredholm integral equations (LSFIEs); Resolvent kernel; Phase-lag.
Journal: J. Fixed Point Theory Appl.
Volume: 20
Issue: 1
Pages: Not Available
Publisher: Springer International Publishing AG, part of Springer Nature 2018
Local/International: International
Paper Link:
Full paper Not Available
Supplementary materials Not Available

This paper presents a numerical method for solving a mixed Fredholm–Volterra linear integral equation of the second kind in a Banach space. Under certain conditions, the existence and uniqueness of the solution are proved, using Banach’s fixed point theorem. Using Nystrom’s method, the problem is reduced to a system of linear integral equations, whose solution is then found by the resolvent method. The ideas are interesting and this area caught the attention of many researchers, having so many applications. This paper starts with a brief introduction in the subject and then proposes a new scheme which is discussed in details. The numerical examples in Sect. 6 illustrate the applicability of the theoretical results.

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