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

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

doi:10.3934/math.2020152

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	2295-2306
Number of pages	12
Journal	AIMS Mathematics
Volume	5
Issue number	3
DOIs	https://doi.org/10.3934/math.2020152
State	Published - 2020

Keywords

2D Bernstein’s approximation
2D Fredholm integral equations
Convergence analysis
Discretization
Numerical solution

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10.3934/math.2020152

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title = "Numerical solutions of 2D fredholm integral equation of first kind by discretization technique",

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.",

keywords = "2D Bernstein{\textquoteright}s approximation, 2D Fredholm integral equations, Convergence analysis, Discretization, Numerical solution",

author = "Faheem Khan and Tayyaba Arshad and Abdul Ghaffar and Nisar, \{Kottakkaran Sooppy\} and Devendra Kumar",

note = "Publisher Copyright: {\textcopyright} 2020 the Author(s), licensee AIMS Press.",

year = "2020",

doi = "10.3934/math.2020152",

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volume = "5",

pages = "2295--2306",

journal = "AIMS Mathematics",

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publisher = "American Institute of Mathematical Sciences",

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T1 - Numerical solutions of 2D fredholm integral equation of first kind by discretization technique

AU - Khan, Faheem

AU - Arshad, Tayyaba

AU - Ghaffar, Abdul

AU - Nisar, Kottakkaran Sooppy

AU - Kumar, Devendra

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - 2D Bernstein’s approximation

KW - 2D Fredholm integral equations

KW - Convergence analysis

KW - Discretization

KW - Numerical solution

UR - https://www.scopus.com/pages/publications/85083091819

U2 - 10.3934/math.2020152

DO - 10.3934/math.2020152

M3 - Article

AN - SCOPUS:85083091819

SN - 2473-6988

VL - 5

SP - 2295

EP - 2306

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 3

ER -

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

Abstract

Keywords

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