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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |