A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications
The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck"...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/12/665 |
| _version_ | 1797461484815515648 |
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| author | Muhammad Nadeem Ali Akgül Liliana Guran Monica-Felicia Bota |
| author_facet | Muhammad Nadeem Ali Akgül Liliana Guran Monica-Felicia Bota |
| author_sort | Muhammad Nadeem |
| collection | DOAJ |
| description | The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">A</mi></mrow></semantics></math></inline-formula>HITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">A</mi></mrow></semantics></math></inline-formula>IT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach. |
| first_indexed | 2024-03-09T17:20:04Z |
| format | Article |
| id | doaj.art-5903b87176a64b0584291b5859f93233 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:20:04Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5903b87176a64b0584291b5859f932332023-11-24T13:15:01ZengMDPI AGAxioms2075-16802022-11-01111266510.3390/axioms11120665A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational ApplicationsMuhammad Nadeem0Ali Akgül1Liliana Guran2Monica-Felicia Bota3School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, ChinaDepartment of Computer Science and Mathematics, Lebanese American University, Beirut 1102 2801, LebanonDepartment of Pharmaceutical Sciences, “Vasile Goldis” Western University of Arad, L. Rebreanu Street, No. 86, 310048 Arad, RomaniaDepartment of Mathematics, Babes-Bolyai University, M. Kogălniceanu Street, No. 1, 400084 Cluj-Napoca, RomaniaThe main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">A</mi></mrow></semantics></math></inline-formula>HITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">A</mi></mrow></semantics></math></inline-formula>IT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach.https://www.mdpi.com/2075-1680/11/12/665Aboodh integral transformhomotopy perturbation methodwave problemsseries results |
| spellingShingle | Muhammad Nadeem Ali Akgül Liliana Guran Monica-Felicia Bota A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications Axioms Aboodh integral transform homotopy perturbation method wave problems series results |
| title | A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications |
| title_full | A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications |
| title_fullStr | A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications |
| title_full_unstemmed | A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications |
| title_short | A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications |
| title_sort | novel approach for the approximate solution of wave problems in multi dimensional orders with computational applications |
| topic | Aboodh integral transform homotopy perturbation method wave problems series results |
| url | https://www.mdpi.com/2075-1680/11/12/665 |
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