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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/23/3858 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850107272012759040 |
|---|---|
| author | Mariusz Pleszczyński Konrad Kaczmarek Damian Słota |
| author_facet | Mariusz Pleszczyński Konrad Kaczmarek Damian Słota |
| author_sort | Mariusz Pleszczyński |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4772ab17af37486cb5e44e2de0669b62 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4772ab17af37486cb5e44e2de0669b622025-08-20T02:38:36ZengMDPI AGMathematics2227-73902024-12-011223385810.3390/math12233858Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch ProblemMariusz Pleszczyński0Konrad Kaczmarek1Damian Słota2Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandDepartment of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandDepartment of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandThe 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.https://www.mdpi.com/2227-7390/12/23/3858Troesch problemDTMAdomian decomposition methoddifferential equations |
| spellingShingle | Mariusz Pleszczyński Konrad Kaczmarek Damian Słota Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem Mathematics Troesch problem DTM Adomian decomposition method differential equations |
| title | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
| title_full | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
| title_fullStr | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
| title_full_unstemmed | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
| title_short | Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem |
| title_sort | application of a hybrid of the different transform method and adomian decomposition method algorithms to solve the troesch problem |
| topic | Troesch problem DTM Adomian decomposition method differential equations |
| url | https://www.mdpi.com/2227-7390/12/23/3858 |
| work_keys_str_mv | AT mariuszpleszczynski applicationofahybridofthedifferenttransformmethodandadomiandecompositionmethodalgorithmstosolvethetroeschproblem AT konradkaczmarek applicationofahybridofthedifferenttransformmethodandadomiandecompositionmethodalgorithmstosolvethetroeschproblem AT damiansłota applicationofahybridofthedifferenttransformmethodandadomiandecompositionmethodalgorithmstosolvethetroeschproblem |