Discrete first-order three-point boundary value problem
We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Canadian Center of Science and Education
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/14086/1/14086.pdf |
| _version_ | 1796968572882255872 |
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| author | Mohamed, Mesliza Thompson, Bevan Jusoh, Muhammad Sufian Jusoff, Kamaruzaman |
| author_facet | Mohamed, Mesliza Thompson, Bevan Jusoh, Muhammad Sufian Jusoff, Kamaruzaman |
| author_sort | Mohamed, Mesliza |
| collection | UPM |
| description | We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euclidean space. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. We also give some examples to illustrate the existence of a unique solution of the contraction mapping theorem. |
| first_indexed | 2024-03-06T07:30:17Z |
| format | Article |
| id | upm.eprints-14086 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:30:17Z |
| publishDate | 2009 |
| publisher | Canadian Center of Science and Education |
| record_format | dspace |
| spelling | upm.eprints-140862020-07-14T04:27:52Z http://psasir.upm.edu.my/id/eprint/14086/ Discrete first-order three-point boundary value problem Mohamed, Mesliza Thompson, Bevan Jusoh, Muhammad Sufian Jusoff, Kamaruzaman We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euclidean space. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. We also give some examples to illustrate the existence of a unique solution of the contraction mapping theorem. Canadian Center of Science and Education 2009 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/14086/1/14086.pdf Mohamed, Mesliza and Thompson, Bevan and Jusoh, Muhammad Sufian and Jusoff, Kamaruzaman (2009) Discrete first-order three-point boundary value problem. Journal of Mathematics Research, 1 (2). pp. 207-215. ISSN 1916-9795; ESSN: 1916-9809 http://www.ccsenet.org/journal/index.php/jmr/article/view/3794 10.5539/jmr.v1n2p207 |
| spellingShingle | Mohamed, Mesliza Thompson, Bevan Jusoh, Muhammad Sufian Jusoff, Kamaruzaman Discrete first-order three-point boundary value problem |
| title | Discrete first-order three-point boundary value problem |
| title_full | Discrete first-order three-point boundary value problem |
| title_fullStr | Discrete first-order three-point boundary value problem |
| title_full_unstemmed | Discrete first-order three-point boundary value problem |
| title_short | Discrete first-order three-point boundary value problem |
| title_sort | discrete first order three point boundary value problem |
| url | http://psasir.upm.edu.my/id/eprint/14086/1/14086.pdf |
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