Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials
We aim through this paper to present an improved variational iteration method (VIM) based on Bernstein polynomials (BP) approximations to be used with transcendental functions. The key benefits gained from this modification are to reach stable and fairly accurate results and, at the same time, to ex...
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Series: | International Journal of Mathematics and Mathematical Sciences |
Online Access: | http://dx.doi.org/10.1155/2019/2872867 |
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doaj-5f34b3972b30482ab60c854017a160202020-11-25T02:22:49ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/28728672872867Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein PolynomialsAhmed Farooq Qasim0Almutasim Abdulmuhsin Hamed1College of Computer Sciences and Mathematics, University of Mosul, IraqCollege of Computer Sciences and Mathematics, University of Mosul, IraqWe aim through this paper to present an improved variational iteration method (VIM) based on Bernstein polynomials (BP) approximations to be used with transcendental functions. The key benefits gained from this modification are to reach stable and fairly accurate results and, at the same time, to expand the unknown function’s domain in partial differential equations (PDEs). The proposed approach introduces the Bernstein polynomials in the transcendental functions of nonlinear PDEs. A number of examples were included in order to expound the method’s capacity and reliability. From the results, we conclude that the VIM with BP is a powerful mathematical tool that can be applied to solve nonlinear PDEs.http://dx.doi.org/10.1155/2019/2872867 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ahmed Farooq Qasim Almutasim Abdulmuhsin Hamed |
spellingShingle |
Ahmed Farooq Qasim Almutasim Abdulmuhsin Hamed Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials International Journal of Mathematics and Mathematical Sciences |
author_facet |
Ahmed Farooq Qasim Almutasim Abdulmuhsin Hamed |
author_sort |
Ahmed Farooq Qasim |
title |
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials |
title_short |
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials |
title_full |
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials |
title_fullStr |
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials |
title_full_unstemmed |
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials |
title_sort |
treating transcendental functions in partial differential equations using the variational iteration method with bernstein polynomials |
publisher |
Hindawi Limited |
series |
International Journal of Mathematics and Mathematical Sciences |
issn |
0161-1712 1687-0425 |
publishDate |
2019-01-01 |
description |
We aim through this paper to present an improved variational iteration method (VIM) based on Bernstein polynomials (BP) approximations to be used with transcendental functions. The key benefits gained from this modification are to reach stable and fairly accurate results and, at the same time, to expand the unknown function’s domain in partial differential equations (PDEs). The proposed approach introduces the Bernstein polynomials in the transcendental functions of nonlinear PDEs. A number of examples were included in order to expound the method’s capacity and reliability. From the results, we conclude that the VIM with BP is a powerful mathematical tool that can be applied to solve nonlinear PDEs. |
url |
http://dx.doi.org/10.1155/2019/2872867 |
work_keys_str_mv |
AT ahmedfarooqqasim treatingtranscendentalfunctionsinpartialdifferentialequationsusingthevariationaliterationmethodwithbernsteinpolynomials AT almutasimabdulmuhsinhamed treatingtranscendentalfunctionsinpartialdifferentialequationsusingthevariationaliterationmethodwithbernsteinpolynomials |
_version_ |
1724861557492416512 |