A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations
In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the conver...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2020-06-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/A-Review-Differential-Transform-Method-for-Semi-Analytical-Solution-of-Differential,166858,0,2.html |
| _version_ | 1797750463726092288 |
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| author | M.M. Rashidi F. Rabiei S. Naseri Nia S. Abbasbandy |
| author_facet | M.M. Rashidi F. Rabiei S. Naseri Nia S. Abbasbandy |
| author_sort | M.M. Rashidi |
| collection | DOAJ |
| description | In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed. |
| first_indexed | 2024-03-12T16:33:05Z |
| format | Article |
| id | doaj.art-041907b439984d1a90df8ba0acdf460f |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:33:05Z |
| publishDate | 2020-06-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-041907b439984d1a90df8ba0acdf460f2023-08-08T15:02:50ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032020-06-0125212212910.2478/ijame-2020-0024166858A Review: Differential Transform Method for Semi-Analytical Solution of Differential EquationsM.M. Rashidi0F. Rabiei1S. Naseri Nia2S. Abbasbandy3Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, ChinaSchool of Engineering, Monash University Malaysia, 47500, Selangor, MalaysiaSchool of Engineering, Monash University Malaysia, 47500, Selangor, MalaysiaDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, IranIn this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.https://www.ijame-poland.com/A-Review-Differential-Transform-Method-for-Semi-Analytical-Solution-of-Differential,166858,0,2.htmldifferential transform methoddifferential transform-pad é approximationsemi-analytical methoddifferential equationsfuzzy differential transformation methodgs-differentiability |
| spellingShingle | M.M. Rashidi F. Rabiei S. Naseri Nia S. Abbasbandy A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations International Journal of Applied Mechanics and Engineering differential transform method differential transform-pad é approximation semi-analytical method differential equations fuzzy differential transformation method gs-differentiability |
| title | A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations |
| title_full | A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations |
| title_fullStr | A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations |
| title_full_unstemmed | A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations |
| title_short | A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations |
| title_sort | review differential transform method for semi analytical solution of differential equations |
| topic | differential transform method differential transform-pad é approximation semi-analytical method differential equations fuzzy differential transformation method gs-differentiability |
| url | https://www.ijame-poland.com/A-Review-Differential-Transform-Method-for-Semi-Analytical-Solution-of-Differential,166858,0,2.html |
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