Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique

A novel numerical technique to solve 2D Fredholm integral equations (2DFIEs) of first kind is proposed in this study. This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence anal...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 3; pp. 2295 - 2306
Main Authors Khan, Faheem, Arshad, Tayyaba, Ghaffar, Abdul, Sooppy Nisar, Kottakkaran, Kumar, Devendra
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
2d bernstein’s approximation
2d fredholm integral equations
convergence analysis
discretization
numerical solution
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ISSN2473-6988
2473-6988
DOI10.3934/math.2020152

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Summary:A novel numerical technique to solve 2D Fredholm integral equations (2DFIEs) of first kind is proposed in this study. This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence analysis which shows the fast converges of this technique to the actual solution. Some problems of 2D linear Fredholm integral equations are illustrated to show the efficiency of the proposed scheme.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020152