Optimal variational iteration method for parametric boundary value problem

Qura Tul Ain; Muhammad Nadeem; Shazia Karim; Ali Akgül; Fahd Jarad; Qura Tul Ain; Muhammad Nadeem; Shazia Karim; Ali Akgül; Fahd Jarad

doi:10.3934/math.2022912

AIMS Mathematics

2022, Volume 7, Issue 9: 16649-16656. doi: 10.3934/math.2022912

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Research article

Optimal variational iteration method for parametric boundary value problem

1.
Department of Mathematics, Guizhou University, Guiyang 550025, China
2.
Faculty of Science, Yibin University, 644000, Yibin, China
3.
Department of Basic Sciences, FSD Campus, UET Lahore, Pakistan
4.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
5.
Department of Mathematics, Çankaya University, 06790, Etimesgut, Ankara, Turkey
6.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
7.
Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

Received: 11 April 2022 Revised: 20 June 2022 Accepted: 30 June 2022 Published: 12 July 2022
MSC : 34B05, 65K05

Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.
- boundary value problem,
- h-curves,
- residual error method,
- optimal variational iteration method
Citation: Qura Tul Ain, Muhammad Nadeem, Shazia Karim, Ali Akgül, Fahd Jarad. Optimal variational iteration method for parametric boundary value problem[J]. AIMS Mathematics, 2022, 7(9): 16649-16656. doi: 10.3934/math.2022912

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Abstract

Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.

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