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

Document Type : Original Article

Authors

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

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


Volume 1, Issue 1
February 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