Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials

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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Main Authors: Ahmed Farooq Qasim, Almutasim Abdulmuhsin Hamed
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2019/2872867
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spelling 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
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