Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

An effective technique for solving generalized Cahn-Hilliard (C-H) problems.

Document Type : Original Article

Authors
A. Hassan 1
A. A. M. Arafa 2
S. Z. Rida 3
M. A. Dagher 4
H. M. El Sherbiny 5
1 Department of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez University, P. O. Box: 43221, Suez, Egypt
2 Department of Mathematics, College of Science and Arts, Qassim University, Al Mithnab, Saudi Arabia - Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt
3 Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
4 Department of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez University, P. O. Box: 43221, Suez, Egypt - Faculty of Engineering, King Salman International University, El-Tor, Egypt
5 Department of Mathematics and Computer Science, Faculty of Science, Suez University, P. O. Box: 43221, Suez, Egypt
10.30511/ttmp.2024.709795
Abstract
Throughout this paper, we apply the Optimal Homotopy Asymptotic Method (OHAM) to find out the numerical solutions of the fractional Cahn-Hilliard (C-H) equation. We examine fractional order time dependent partial differential equations to assess the method's competency. In the Caputo sense, fractional-order derivatives have been applied with numerical values in the closed interval [0, 1]. The most advantage of this method is that it contains parameters that strongly control the solution series convergence. Additionally, this method greatly simplifies calculations because it does not require any linearization, discretization, or little perturbations. Approximate solutions of the C-H equation were compared with the exact solutions; moreover the results of the suggested method have been compared with those of other widely used numerical techniques, such as the Adomian decomposition analysis method. A comparison of these solutions with the exact solution shows that our method is more effective and accurate for solving nonlinear differential equations. MATLAB R2021b is utilized to generate the numerical results.
Keywords
Cahn&ndash
Hilliard equation
Fractional calculus
Optimal Homotopy Asymptotic Method
Numerical solutions
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Transactions in Theoretical and Mathematical Physics
Volume 1, Issue 1
Winter 2024
Pages 1-8

  • Receive Date 12 August 2023
  • Revise Date 09 October 2023
  • Accept Date 04 November 2023
  • First Publish Date 04 January 2024
  • Publish Date 01 February 2024