Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method
This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/6/247 |
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| author | Shams A. Ahmed Ahmad Qazza Rania Saadeh |
| author_facet | Shams A. Ahmed Ahmad Qazza Rania Saadeh |
| author_sort | Shams A. Ahmed |
| collection | DOAJ |
| description | This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs. |
| first_indexed | 2024-03-10T00:26:10Z |
| format | Article |
| id | doaj.art-e74b7ac004984349aecc8b56f29a5abd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T00:26:10Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e74b7ac004984349aecc8b56f29a5abd2023-11-23T15:34:52ZengMDPI AGAxioms2075-16802022-05-0111624710.3390/axioms11060247Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative MethodShams A. Ahmed0Ahmad Qazza1Rania Saadeh2Department of Mathematic, Faculty of Sciences and Arts, Jouf University, Tubarjal 74756, Saudi ArabiaDepartment of Mathematics, Zarqa University, Zarqa 13110, JordanDepartment of Mathematics, Zarqa University, Zarqa 13110, JordanThis article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.https://www.mdpi.com/2075-1680/11/6/247double Laplace–Sumudu transformsingle Laplace transformsingle Sumudu transformnew iterative methodnonlinear partial differential equations |
| spellingShingle | Shams A. Ahmed Ahmad Qazza Rania Saadeh Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method Axioms double Laplace–Sumudu transform single Laplace transform single Sumudu transform new iterative method nonlinear partial differential equations |
| title | Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method |
| title_full | Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method |
| title_fullStr | Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method |
| title_full_unstemmed | Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method |
| title_short | Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method |
| title_sort | exact solutions of nonlinear partial differential equations via the new double integral transform combined with iterative method |
| topic | double Laplace–Sumudu transform single Laplace transform single Sumudu transform new iterative method nonlinear partial differential equations |
| url | https://www.mdpi.com/2075-1680/11/6/247 |
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