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

Faheem Khan; Tayyaba Arshad; Abdul Ghaffar; Kottakkaran Sooppy Nisar; Devendra Kumar; Faheem Khan; Tayyaba Arshad; Abdul Ghaffar; Kottakkaran Sooppy Nisar; Devendra Kumar

doi:10.3934/math.2020152

AIMS Mathematics

2020, Volume 5, Issue 3: 2295-2306. doi: 10.3934/math.2020152

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

1.
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2.
Faculty of Mathematics & Statistics, Ton Duc Thang University, Hu Chi Minh City, Vietnam
3.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
4.
Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India

Received: 18 October 2019 Accepted: 27 February 2020 Published: 02 March 2020
MSC : 65A05, 65G99, 65R20

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.
- discretization,
- numerical solution,
- 2D Fredholm integral equations,
- 2D Bernstein’s approximation,
- convergence analysis
Citation: Faheem Khan, Tayyaba Arshad, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique[J]. AIMS Mathematics, 2020, 5(3): 2295-2306. doi: 10.3934/math.2020152

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Abstract

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.

References

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