A new application of the Legendre reproducing kernel method

Mohammad Reza Foroutan; Mir Sajjad Hashemi; Leila Gholizadeh; Ali Akgül; Fahd Jarad; Mohammad Reza Foroutan; Mir Sajjad Hashemi; Leila Gholizadeh; Ali Akgül; Fahd Jarad

doi:10.3934/math.2022594

AIMS Mathematics

2022, Volume 7, Issue 6: 10651-10670. doi: 10.3934/math.2022594

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Research article Special Issues

A new application of the Legendre reproducing kernel method

1.
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
2.
Department of Mathematics, University of Bonab, P.O. Box 55513-95133, Bonab, Iran
3.
Art and Science Faculty, Department of Mathematics, Siirt University, TR-56100, Siirt, Turkey
4.
Department of Mathematics, Çankaya University, Ankara 06790, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 24 December 2021 Revised: 10 March 2022 Accepted: 15 March 2022 Published: 30 March 2022
MSC : 35A24, 46E20, 47B32

In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
- Legendre polynomials,
- reproducing kernel functions,
- approximate solution,
- convergence analysis,
- boundary value problem
Citation: Mohammad Reza Foroutan, Mir Sajjad Hashemi, Leila Gholizadeh, Ali Akgül, Fahd Jarad. A new application of the Legendre reproducing kernel method[J]. AIMS Mathematics, 2022, 7(6): 10651-10670. doi: 10.3934/math.2022594

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Abstract

In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.

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