Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations
This paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2017-12-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.5008818 |
| _version_ | 1818276393346138112 |
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| author | Faheem Khan Ghulam Mustafa Muhammad Omar Haziqa Komal |
| author_facet | Faheem Khan Ghulam Mustafa Muhammad Omar Haziqa Komal |
| author_sort | Faheem Khan |
| collection | DOAJ |
| description | This paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and Engineering models. The proposed method is based on the discretization of VFIEs by Bernstein’s approximation. Some results on convergence are also established which suggests that the technique converges to a smooth approximate solution. Its remarkable accuracy properties are finally demonstrated by several examples with graphical representation. |
| first_indexed | 2024-12-12T22:44:56Z |
| format | Article |
| id | doaj.art-c9443e767d5648d984cdabc5fba9b140 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-12T22:44:56Z |
| publishDate | 2017-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-c9443e767d5648d984cdabc5fba9b1402022-12-22T00:09:14ZengAIP Publishing LLCAIP Advances2158-32262017-12-01712125123125123-1410.1063/1.5008818075712ADVNumerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equationsFaheem Khan0Ghulam Mustafa1Muhammad Omar2Haziqa Komal3Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, 63100, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, 57000, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanThis paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and Engineering models. The proposed method is based on the discretization of VFIEs by Bernstein’s approximation. Some results on convergence are also established which suggests that the technique converges to a smooth approximate solution. Its remarkable accuracy properties are finally demonstrated by several examples with graphical representation.http://dx.doi.org/10.1063/1.5008818 |
| spellingShingle | Faheem Khan Ghulam Mustafa Muhammad Omar Haziqa Komal Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations AIP Advances |
| title | Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations |
| title_full | Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations |
| title_fullStr | Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations |
| title_full_unstemmed | Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations |
| title_short | Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations |
| title_sort | numerical approach based on bernstein polynomials for solving mixed volterra fredholm integral equations |
| url | http://dx.doi.org/10.1063/1.5008818 |
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