Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm
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 predict changes in physical systems. Solutions of such equations require efficient and effective techniques to get rea...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-05-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682300193X |
| _version_ | 1797854517286404096 |
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| author | Mubashir Qayyum Amna Khan Syed Tauseef Saeed Ali Akgül Muhammad Bilal Riaz |
| author_facet | Mubashir Qayyum Amna Khan Syed Tauseef Saeed Ali Akgül Muhammad Bilal Riaz |
| author_sort | Mubashir Qayyum |
| collection | DOAJ |
| description | 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 predict changes in physical systems. Solutions of such equations require efficient and effective techniques 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 computed. In next stage of testing, proposed algorithm is enforced to three-dimensional non–homogeneous 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. |
| first_indexed | 2024-04-09T20:08:25Z |
| format | Article |
| id | doaj.art-284bbfe67229458f960c01b4b85217da |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T20:08:25Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-284bbfe67229458f960c01b4b85217da2023-04-01T08:45:44ZengElsevierAlexandria Engineering Journal1110-01682023-05-0171479489Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithmMubashir Qayyum0Amna Khan1Syed Tauseef Saeed2Ali Akgül3Muhammad Bilal Riaz4Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulenvard, PC:99138 Nicosia/Mersin 10, TurkeyDepartment of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon; Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland; Department of Mathematics, University of Management and Technology, 54770 Lahore, Pakistan; Corresponding author at: Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland.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 predict changes in physical systems. Solutions of such equations require efficient and effective techniques 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 computed. In next stage of testing, proposed algorithm is enforced to three-dimensional non–homogeneous 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.http://www.sciencedirect.com/science/article/pii/S111001682300193XPartial differential equationsResidual power seriesParabolic equationsSeries solution |
| spellingShingle | Mubashir Qayyum Amna Khan Syed Tauseef Saeed Ali Akgül Muhammad Bilal Riaz Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm Alexandria Engineering Journal Partial differential equations Residual power series Parabolic equations Series solution |
| title | Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm |
| title_full | Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm |
| title_fullStr | Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm |
| title_full_unstemmed | Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm |
| title_short | Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm |
| title_sort | closed form solutions of higher order parabolic equations in multiple dimensions a reliable computational algorithm |
| topic | Partial differential equations Residual power series Parabolic equations Series solution |
| url | http://www.sciencedirect.com/science/article/pii/S111001682300193X |
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