Efficient schemes on solving fractional integro-differential equations
Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after....
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| Format: | Thesis |
| Language: | English English English |
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2018
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| Online Access: | http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf |
| _version_ | 1796868225130037248 |
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| author | Loh, Jian Rong |
| author_facet | Loh, Jian Rong |
| author_sort | Loh, Jian Rong |
| collection | UTHM |
| description | Fractional integro-differential equation (FIDE) emerges in various modelling of
physical phenomena. In most cases, finding the exact analytical solution for FIDE is
difficult or not possible. Hence, the methods producing highly accurate numerical
solution in efficient ways are often sought after. This research has designed some
methods to find the approximate solution of FIDE. The analytical expression of
Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s
derivative and kernel matrix has been derived. Linear independence of Genocchi
polynomials has been proved by deriving the expression for Genocchi polynomial
Gram determinant. Genocchi polynomial method with collocation has been
introduced and applied in solving both linear and system of linear FIDE. The
numerical results of solving linear FIDE by Genocchi polynomial are compared with
certain existing methods. The analytical expression of Bernoulli polynomial
operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli
expansion coefficient for a two-variable function is derived. Linear FIDE with mixed
left and right-sided Caputo’s derivative is first considered and solved by applying the
Bernoulli polynomial with spectral-tau method. Numerical results obtained show that
the method proposed achieves very high accuracy. The upper bounds for the |
| first_indexed | 2024-03-05T21:36:38Z |
| format | Thesis |
| id | uthm.eprints-204 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | English English English |
| last_indexed | 2024-03-05T21:36:38Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | uthm.eprints-2042021-07-06T08:22:08Z http://eprints.uthm.edu.my/204/ Efficient schemes on solving fractional integro-differential equations Loh, Jian Rong QA Mathematics Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for the 2018-02 Thesis NonPeerReviewed text en http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf text en http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf text en http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf Loh, Jian Rong (2018) Efficient schemes on solving fractional integro-differential equations. Doctoral thesis, Universiti Tun Hussein Onn Malaysia. |
| spellingShingle | QA Mathematics Loh, Jian Rong Efficient schemes on solving fractional integro-differential equations |
| title | Efficient schemes on solving fractional integro-differential equations |
| title_full | Efficient schemes on solving fractional integro-differential equations |
| title_fullStr | Efficient schemes on solving fractional integro-differential equations |
| title_full_unstemmed | Efficient schemes on solving fractional integro-differential equations |
| title_short | Efficient schemes on solving fractional integro-differential equations |
| title_sort | efficient schemes on solving fractional integro differential equations |
| topic | QA Mathematics |
| url | http://eprints.uthm.edu.my/204/1/LOH%20JIAN%20RONG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/204/2/LOH%20JIAN%20RONG%20WATERMARK.pdf http://eprints.uthm.edu.my/204/3/24p%20LOH%20JIAN%20RONG.pdf |
| work_keys_str_mv | AT lohjianrong efficientschemesonsolvingfractionalintegrodifferentialequations |