Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences

Majeed A. Al-Jawary; Ghada H. Ibraheem

doi:https://doi.org/10.1515/nleng-2020-0012

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Publication Date

Wed May 13 2020

Journal Name

Nonlinear Engineering

Volume

9

DOI

https://doi.org/10.1515/nleng-2020-0012

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Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences

Majeed A. Al-Jawary

Ghada H. Ibraheem

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Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To illustrate the accuracy and efficiency of the proposed methods, the maximum error remainder is calculated. The results shown that the proposed methods are accurate, reliable, time saving and effective. In addition, the approximate solutions are compared with the fourth order Runge-Kutta method (RK4) achieving good agreements.</p>

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Publication Date

Sat Jan 01 2022

Journal Name

Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees21gr

AIP Conference Proceedings 2437, 020060 (2022); https://doi.org/10.1063/5.0092690 2437, 020060© 2022 Author(s).Theoretical calculation of the electroniccurrent at N3 contact with TiO2 solar celldevices (3) (PDF) Theoretical calculation of the electronic current at N 3 contact with TiO 2 solar cell devices ARTICLES YOU MAY BE INTERESTED IN Theoretical studies of electronic transition characteristics of senstizer molecule dye N3-SnO 2 semiconductor interface AIP Conference. Available from: https://www.researchgate.net/publication/362813854_Theoretical_calculation_of_the_electronic_current_at_N_3_contact_with_TiO_2_solar_cell_devices_ARTICLES_YOU_MAY_BE_INTERESTED_IN_Theoretical_studies_of_electronic_transition_characteristics_of_senstiz [accessed May 01 2023].

Theoretical calculation

electronic current

N 3 - TiO 2 solar cell

Hadi J.

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Theoretical calculation of the electronic current at N 3 contact with TiO 2 solar cell devices ARTICLES YOU MAY BE INTERESTED IN Theoretical studies of electronic transition characteristics of senstizer molecule dye N3-SnO 2 semiconductor interface AIP Conference. Available from: https://www.researchgate.net/publication/362813854_Theoretical_calculation_of_the_electronic_current_at_N_3_contact_with_TiO_2_solar_cell_devices_ARTICLES_YOU_MAY_BE_INTERESTED_IN_Theoretical_studies_of_electronic_transition_characteristics_of_senstiz [accessed May 01 2023].

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