Modified homotopy perturbation method for integro-differential and hypersingular integral equations
Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHP...
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my-upm-ir.835652022-01-06T03:18:59Z Modified homotopy perturbation method for integro-differential and hypersingular integral equations 2018-04 Zulkarnain, Fatimah Samihah Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHPM) are obtained in the class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D) where D is a closed subspace of R2 for higher order FVIDE problem. Many researchers solved singular integral equation with kernel equal to one. This study describes the implementation of HPM and MHPM on HSIE of the first kind with kernel is a constant on a diagonal. Convergence and error estimation are obtained in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second kind. For all cases, numerical examples are provided to exhibit the efficiency of the methods. The results obtained are more accurate than the previous works. Mathematics Homotopy equivalences 2018-04 Thesis http://psasir.upm.edu.my/id/eprint/83565/ http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf text en public doctoral Universiti Putra Malaysia Mathematics Homotopy equivalences Nik Long, Nik Mohd Asri |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English |
| advisor |
Nik Long, Nik Mohd Asri |
| topic |
Mathematics Homotopy equivalences |
| spellingShingle |
Mathematics Homotopy equivalences Zulkarnain, Fatimah Samihah Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| description |
Homotopy perturbation method (HPM) is implemented to solve the mathematical
problems. The solution is obtained by taking the summation of infinite series. This
thesis present a modification of HPM by equating the second series as zero. Convergence
and error estimation of HPM and modified HPM (MHPM) are obtained in the
class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D)
where D is a closed subspace of R2 for higher order FVIDE problem.
Many researchers solved singular integral equation with kernel equal to one. This
study describes the implementation of HPM and MHPM on HSIE of the first kind
with kernel is a constant on a diagonal. Convergence and error estimation are obtained
in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second
kind.
For all cases, numerical examples are provided to exhibit the efficiency of the methods.
The results obtained are more accurate than the previous works. |
| format |
Thesis |
| qualification_level |
Doctorate |
| author |
Zulkarnain, Fatimah Samihah |
| author_facet |
Zulkarnain, Fatimah Samihah |
| author_sort |
Zulkarnain, Fatimah Samihah |
| title |
Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_short |
Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_full |
Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_fullStr |
Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_full_unstemmed |
Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_sort |
modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| granting_institution |
Universiti Putra Malaysia |
| publishDate |
2018 |
| url |
http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf |
| _version_ |
1747813397264596992 |