Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm
[ X ]
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Parabolic equations play an important role in chemical engineering, vibration theory, particle diffusion and heat conduction. Solutions of such equations are required to analyze and pre-dict changes in physical systems. Solutions of such equations require efficient and effective tech-niques to get reasonable accuracy in lesser time. For this purpose, current article proposes residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions. The proposed algorithm provides closed-form solutions without linearization, discretization or perturbation. For efficiency testing of the proposed methodology, initially it is implemented to homogeneous multidimensional parabolic models, and exact solutions are com-puted. In next stage of testing, proposed algorithm is enforced to three-dimensional non-homoge-neous fourth order parabolic equation, and closed form solutions are recovered. The obtained results indicate the validity and effectiveness of proposed methodology, hence proposed algorithm can be extended to more complex scenarios in engineering and sciences. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Açıklama
Anahtar Kelimeler
Partial differential equations, Residual power series, Parabolic equations, Series solution
Kaynak
Alexandria Engineering Journal
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
71
