Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem
The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decom...
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| Published in | Mathematics (Basel) Vol. 12; no. 23; p. 3858 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.12.2024
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| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math12233858 |
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| Abstract | The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decomposition Method (ADM). The combination of these two methods resulted in a continuous approximate solution to this problem and eliminated the problems that occur when trying to use each of these methods separately. The great advantages of the DTM method are the continuous form of the solution and the fact that it easy to implement error control. However, in too-complex tasks, this method becomes difficult to use. By using a hybrid of ADM and DTM, we obtain a relatively simple-to-implement method that retains the advantages of the DTM approach. |
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| AbstractList | The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decomposition Method (ADM). The combination of these two methods resulted in a continuous approximate solution to this problem and eliminated the problems that occur when trying to use each of these methods separately. The great advantages of the DTM method are the continuous form of the solution and the fact that it easy to implement error control. However, in too-complex tasks, this method becomes difficult to use. By using a hybrid of ADM and DTM, we obtain a relatively simple-to-implement method that retains the advantages of the DTM approach. |
| Audience | Academic |
| Author | Słota, Damian Kaczmarek, Konrad Pleszczyński, Mariusz |
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| Cites_doi | 10.1080/0020716022000009228 10.1016/j.mcm.2006.07.010 10.1016/j.mcm.2007.12.022 10.3390/math9161841 10.1016/0021-9991(76)90025-5 10.3390/math12142182 10.1016/S0893-9659(02)00030-7 10.1016/j.jppr.2017.01.001 10.1007/978-94-009-2569-4 10.3390/sym16070856 10.1016/0022-247X(88)90170-9 10.3390/s22114124 10.1006/jcph.2000.6452 10.1016/j.ins.2008.11.016 10.4172/2168-9679.1000109 10.1016/j.ijheatmasstransfer.2013.07.053 10.1080/15502287.2016.1157646 10.3390/math10030306 10.17576/jsm-2017-4610-40 10.1016/j.cam.2010.04.018 10.3390/sym16020233 10.1080/00207160600961729 10.1006/jmaa.1998.6243 10.1155/2012/965367 10.1155/S0161171200002970 10.1016/j.molliq.2013.12.034 10.1016/j.cam.2007.07.033 10.1016/j.ijheatmasstransfer.2004.07.049 10.1016/j.mcm.2011.04.030 10.1080/00207160701224712 |
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| SubjectTerms | Adomian decomposition method Algorithms Decomposition differential equations DTM Integral equations Methods Ordinary differential equations Partial differential equations Polynomials Task complexity Troesch problem |
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| Title | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
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