الوصف

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 biggest 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 lineariza-tion, 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.

URL

DOI

DOI:10.30511/ttmp.2024.709795

الملخص

In this study, we implement OHAM to accurately solve the C-H equations. The accuracy of these re-sults has been shown in Tables (1-5) and they have been shown graphically in Figures (1-3) in order to highlight the efficiency and distinction of this meth-od. The technique convergence is regulated by a flexible function known as the auxiliary function. The Caputo derivative fractional-order and the well-known least squares technique are used to determine the values of the unknown arbitrary constants in the auxiliary function. In the Caputo meaning, fraction-al-order derivatives are taken with results in the closed interval [0, 1]. The proposed technique is immediately applicable to Cahn-Hilliard equations, and no small or large parameter assumptions are required. Also, studies on this topic may lead to more interesting conclusions and results. Thus, it offers more realistic solutions to real physical prob-lems.

الكلمات الدالة

Cahn–Hilliard equation, Fractional calculus; Optimal Homotopy Asymptotic Method; Numerical solutions.