Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method

Abdulghani R. Alharbi; Abdulghani R. Alharbi

doi:10.3934/math.2023841

AIMS Mathematics

2023, Volume 8, Issue 7: 16463-16478. doi: 10.3934/math.2023841

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Research article

Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method

Abdulghani R. Alharbi ^,

Department of Mathematics, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

Received: 27 February 2023 Revised: 24 March 2023 Accepted: 23 April 2023 Published: 09 May 2023
MSC : 35A24, 35B35, 35Q51, 35Q92, 65N06, 65N40, 65N45, 65N50

This article presents the Parabolic-Monge-Ampere (PMA) method for numerical solutions of two-dimensional fourth-order parabolic thin film equations with constant flux boundary conditions. We track the PMA technique, which employs special functions to acclimate and force the mesh moving associated with the physical PDE representing the thin liquid film equation. The accuracy and convergence of the PMA approach are investigated numerically using a one two-dimensional problem. Comparing the results of this method to the uniform mesh finite difference scheme, the computing effort is reduced.
- the thin film flows,
- surface tension,
- Parabolic-Monge-Ampere,
- mesh density function
Citation: Abdulghani R. Alharbi. Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method[J]. AIMS Mathematics, 2023, 8(7): 16463-16478. doi: 10.3934/math.2023841

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Abstract

This article presents the Parabolic-Monge-Ampere (PMA) method for numerical solutions of two-dimensional fourth-order parabolic thin film equations with constant flux boundary conditions. We track the PMA technique, which employs special functions to acclimate and force the mesh moving associated with the physical PDE representing the thin liquid film equation. The accuracy and convergence of the PMA approach are investigated numerically using a one two-dimensional problem. Comparing the results of this method to the uniform mesh finite difference scheme, the computing effort is reduced.

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