Approximate Analytical Methods For Solving Fredholm Integral Equations
| dc.contributor.author | TALEB ALMOUSA, MOHAMMAD SALAMEH | |
| dc.date.accessioned | 2016-04-15T07:22:16Z | |
| dc.date.available | 2016-04-15T07:22:16Z | |
| dc.date.issued | 2015-02 | |
| dc.description.abstract | Integral equations play an important role in many branches of sciences such as mathematics, biology, chemistry, physics, mechanics and engineering. Therefore, many different techniques are used to solve these types of equations. This study focuses on the mathematical and numerical analysis of some cases of linear and nonlinear Fredholm integral equations. These cases are one-dimensional Fredholm integral equations of the first kind and second kind, two-dimensional Fredholm integral equations of the first kind and second kind and systems of one and two-dimensional Fredholm integral equations. In this thesis, approximate analytical methods are proposed to investigate some cases of linear and nonlinear Fredholm integral equations. Such approximate analytical methods include: optimal homotopy asymptotic method (OHAM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). In the first approach, the effectiveness of OHAM is investigated for solving some cases of Fredholm integral equations. The analytical solutions and absolute errors obtained by using this method are tabulated and analyzed and comparison is carried out by using other methods in literature. It was found that the OHAM is faster, easier to implement and more accurate compared to other methods and there is no need of initial guess and large computer memory. In the second and third approaches, HPM and ADM are formulated for solving Fredholm-Hammerstein integral equations and two-dimensional Fredholm integral equations. The results obtained by these methods are compared with OHAM and other methods in literature. It is clear that HPM and ADM are accurate and efficient xvi techniques, HPM is equivalent to ADM with the homotopy H 0 and these methods are special cases of the OHAM in solving these types of equations. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/1897 | |
| dc.subject | Approximate Analytical Methods | en_US |
| dc.subject | For Solving Fredholm Integral Equations | en_US |
| dc.title | Approximate Analytical Methods For Solving Fredholm Integral Equations | en_US |
| dc.type | Thesis | en_US |
Files
License bundle
1 - 1 of 1
Loading...
- Name:
- license.txt
- Size:
- 1.71 KB
- Format:
- Item-specific license agreed upon to submission
- Description: