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The Behaviour of the Maximum and Minimum Error for Fredholm-Volterra Integral Equations in Two-Dimensional Space
Journal of Interdisciplinary Mathematics. • 2020
Publication Information
Authors
M. A. Abdou, G. A. Mosa and M. N. Elhamaky
Keywords
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Journal
Journal of Interdisciplinary Mathematics.
Publisher
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Volume
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Issue
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Pages
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publication.type
International
Paper Link
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Supplementary Materials
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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
(1st 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 (2nd 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 results are represented in group of figures and tables.
using Collocation (CM) and Galerkin (GM) methods by choosing N-linearly independent
functions. The approximate solution is obtained by two techniques; the first technique
(1st 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 (2nd 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 results are represented in group of figures and tables.