Numerical analysis of fractional-order nonlinear Gardner and Cahn-Hilliard equations

Naveed Iqbal; Mohammad Alshammari; Wajaree Weera; Naveed Iqbal; Mohammad Alshammari; Wajaree Weera

doi:10.3934/math.2023281

AIMS Mathematics

2023, Volume 8, Issue 3: 5574-5587. doi: 10.3934/math.2023281

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Research article

Numerical analysis of fractional-order nonlinear Gardner and Cahn-Hilliard equations

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 21 September 2022 Revised: 07 December 2022 Accepted: 11 December 2022 Published: 20 December 2022
MSC : 32B15, 34A34, 35A22, 35A24, 45A10

In this study, the suggested residual power series transform method is used to compute the numerical solution of the fractional-order nonlinear Gardner and Cahn-Hilliard equations and the result is discovered in a fast convergent series. The leverage and efficacy of the suggested technique are demonstrated by the test examples provided. The achieved results are proved graphically. The current method handles the series solution in a sizable admissible domain in a powerful way. It provides a simple means of modifying the solution's convergence zone. Results with graphs expressly demonstrate the effectiveness and abilities of the suggested method.
- residual power series method,
- Laplace transform,
- Gardner and Cahn-Hilliard equations,
- analytical solution
Citation: Naveed Iqbal, Mohammad Alshammari, Wajaree Weera. Numerical analysis of fractional-order nonlinear Gardner and Cahn-Hilliard equations[J]. AIMS Mathematics, 2023, 8(3): 5574-5587. doi: 10.3934/math.2023281

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Abstract

In this study, the suggested residual power series transform method is used to compute the numerical solution of the fractional-order nonlinear Gardner and Cahn-Hilliard equations and the result is discovered in a fast convergent series. The leverage and efficacy of the suggested technique are demonstrated by the test examples provided. The achieved results are proved graphically. The current method handles the series solution in a sizable admissible domain in a powerful way. It provides a simple means of modifying the solution's convergence zone. Results with graphs expressly demonstrate the effectiveness and abilities of the suggested method.

References

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