The enhanced homotopy analysis method was employed to solve the nonlinear time-fractional advection equation, resulting in the derivation of a series of solutions. The objective of this study is to minimize the absolute error by identifying the ideal value for a certain parameter, indicated as h, by the utilization of the residual error (RE) function associated with that parameter. The 3-dimensional graphs illustrating the absolute discrepancies between the solutions obtained from the exact approach and the modified homotopy analysis method have been made using the MAPLE software. Hence, the proposed approach demonstrates efficacy and appropriateness in tackling fractional partial differential equations.
Abbasbandy S. Homotopy analysis method for generalized Benjamin-Bona-Mahony equation. Zeitschrift für angewandte Mathematik und Physik 2008; 59: 51-62.
Abdulaziz O., Hashim I., Saif A. Series solutions of time-fractional PDEs by homotopy analysis method. Differential Equations and Nonlinear Mechanics 2008; 13: 16.
Geliştirilmiş Homotopi Analiz Metodu ile Kesirli Mertebeden Adveksiyon Denkleminin Analizi
Year 2024,
Volume: 7 Issue: 3, 1215 - 1229, 25.06.2024
Doğrusal olmayan zaman-kesirli mertebeden adveksiyon denklemini çözmek için geliştirilmiş homotopi analiz yöntemi kullanıldı ve bu da bir dizi çözümün türetilmesiyle sonuçlandı. Bu çalışmanın amacı, h ile gösterilen belirli bir parametre için o parametreye ilişkin artık hata fonksiyonundan yararlanılarak ideal değeri belirleyerek mutlak hatayı en aza indirmektir. Kesin yaklaşımla elde edilen çözümler ile değiştirilmiş homotopi analiz yöntemi arasındaki mutlak farklılıkları gösteren 3 boyutlu grafikler MAPLE yazılımı kullanılarak yapılmıştır. Dolayısıyla önerilen yaklaşım kesirli kısmi diferansiyel denklemlerin çözümünde etkinlik ve uygunluk göstermektedir.
Abbasbandy S. Homotopy analysis method for generalized Benjamin-Bona-Mahony equation. Zeitschrift für angewandte Mathematik und Physik 2008; 59: 51-62.
Abdulaziz O., Hashim I., Saif A. Series solutions of time-fractional PDEs by homotopy analysis method. Differential Equations and Nonlinear Mechanics 2008; 13: 16.
There are 2 citations in total.
Details
Primary Language
English
Subjects
Numerical Solution of Differential and Integral Equations
Alkan, A. (2024). Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7(3), 1215-1229. https://doi.org/10.47495/okufbed.1387630
AMA
Alkan A. Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. June 2024;7(3):1215-1229. doi:10.47495/okufbed.1387630
Chicago
Alkan, Aslı. “Analysis of Fractional Advection Equation With Improved Homotopy Analysis Method”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7, no. 3 (June 2024): 1215-29. https://doi.org/10.47495/okufbed.1387630.
EndNote
Alkan A (June 1, 2024) Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7 3 1215–1229.
IEEE
A. Alkan, “Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method”, Osmaniye Korkut Ata University Journal of The Institute of Science and Techno, vol. 7, no. 3, pp. 1215–1229, 2024, doi: 10.47495/okufbed.1387630.
ISNAD
Alkan, Aslı. “Analysis of Fractional Advection Equation With Improved Homotopy Analysis Method”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7/3 (June 2024), 1215-1229. https://doi.org/10.47495/okufbed.1387630.
JAMA
Alkan A. Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. 2024;7:1215–1229.
MLA
Alkan, Aslı. “Analysis of Fractional Advection Equation With Improved Homotopy Analysis Method”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 7, no. 3, 2024, pp. 1215-29, doi:10.47495/okufbed.1387630.
Vancouver
Alkan A. Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. 2024;7(3):1215-29.