Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method
In this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solut...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Computational and Mathematical Methods |
| Online Access: | http://dx.doi.org/10.1155/cmm4/7393931 |
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| _version_ | 1846141054000037888 |
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| author | Rabeea Mohammed Hani Darghoth |
| author_facet | Rabeea Mohammed Hani Darghoth |
| author_sort | Rabeea Mohammed Hani Darghoth |
| collection | DOAJ |
| description | In this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solution for two cases of the partial Harry Dym integrodifferential equation. The approximate solutions are illustrated for some chosen values of the arbitrary constants. The efficiency of this semianalytical method is demonstrated through discussing the regions of the domain with small errors as well as by extracting the exact solution from the limit of the approximation. |
| format | Article |
| id | doaj-art-5667b56a4b0b40e28fc16e8dbc97e654 |
| institution | Kabale University |
| issn | 2577-7408 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Computational and Mathematical Methods |
| spelling | doaj-art-5667b56a4b0b40e28fc16e8dbc97e6542024-12-05T00:00:02ZengWileyComputational and Mathematical Methods2577-74082024-01-01202410.1155/cmm4/7393931Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive MethodRabeea Mohammed Hani Darghoth0Department of MathematicsIn this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solution for two cases of the partial Harry Dym integrodifferential equation. The approximate solutions are illustrated for some chosen values of the arbitrary constants. The efficiency of this semianalytical method is demonstrated through discussing the regions of the domain with small errors as well as by extracting the exact solution from the limit of the approximation.http://dx.doi.org/10.1155/cmm4/7393931 |
| spellingShingle | Rabeea Mohammed Hani Darghoth Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method Computational and Mathematical Methods |
| title | Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method |
| title_full | Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method |
| title_fullStr | Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method |
| title_full_unstemmed | Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method |
| title_short | Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method |
| title_sort | approximate solution of an integrodifferential equation generalized by harry dym equation using the picard successive method |
| url | http://dx.doi.org/10.1155/cmm4/7393931 |
| work_keys_str_mv | AT rabeeamohammedhanidarghoth approximatesolutionofanintegrodifferentialequationgeneralizedbyharrydymequationusingthepicardsuccessivemethod |