The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space. Issue 8 (17th November 2021)

• Record Type: Journal Article
• Authors: Abdou, M. A.; Elhamaky, M. N.; Soliman, A. A.; Mosa, G. A.
• Is Part Of: Journal of interdisciplinary mathematics. Volume 24:Issue 8(2021)
• Page Start: 2049
• Page End: 2070
• Publication Date: 2021-11-17
• Subjects: 45L05 -- 46BO7 -- 65R20; Fredholm-Volterra integral equation -- Banach's fixed point theorem -- Collocation method -- Galerkin method -- Maximum error -- Minimum error; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2020.1814497
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: In this paper, we study the behaviour of the maximum ( Max.) and minimum (Min.) error for Fredholm-Volterra integral equations (F-VIEs) of the second kind using Collocation (CM) and Galerkin (GM) methods by choosing N-linearly independent functions. The approximate solution is obtained by two techniques; the first technique (1 st TM) depends on representing F-VIE as a system of Fredholm integral equations (FIEs) of the second kind where the approximate (Appr.) solution is obtained as functions of x at fixed times. In the second technique (2 nd TM), we represent the approximate solution as a sum of functions of x and t . Furthermore, the comparisons between the results which are obtained by two techniques in each method are devoted and the results are represented in group of figures and tables.