Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method
User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/357861 |
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| author | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Maha Al-Humyani |
| author_facet | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Maha Al-Humyani |
| author_sort | Mohamed S. Mohamed |
| collection | DOAJ |
| description | User friendly algorithm based on the optimal homotopy analysis transform method
(OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The
classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that
the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given
to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are
given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the
exact solutions shows that the proposed method is very efficient and computationally attractive. We can use
this method for solving more complicated integral equations in mathematical physical. |
| format | Article |
| id | doaj-art-78a60b3daf56488a8670a2f37b784403 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-78a60b3daf56488a8670a2f37b7844032025-02-03T01:07:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/357861357861Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation MethodMohamed S. Mohamed0Khaled A. Gepreel1Faisal A. Al-Malki2Maha Al-Humyani3Department of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi ArabiaUser friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical.http://dx.doi.org/10.1155/2015/357861 |
| spellingShingle | Mohamed S. Mohamed Khaled A. Gepreel Faisal A. Al-Malki Maha Al-Humyani Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method Journal of Applied Mathematics |
| title | Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method |
| title_full | Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method |
| title_fullStr | Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method |
| title_full_unstemmed | Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method |
| title_short | Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method |
| title_sort | approximate solutions of the generalized abel s integral equations using the extension khan s homotopy analysis transformation method |
| url | http://dx.doi.org/10.1155/2015/357861 |
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