Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/458701 |
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| author | Joan Goh Ahmad Abd. Majid Ahmad Izani Md. Ismail |
| author_facet | Joan Goh Ahmad Abd. Majid Ahmad Izani Md. Ismail |
| author_sort | Joan Goh |
| collection | DOAJ |
| description | Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution. |
| format | Article |
| id | doaj-art-c249b04a417049779744bd48e746b99a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c249b04a417049779744bd48e746b99a2025-02-03T01:33:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/458701458701Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion EquationsJoan Goh0Ahmad Abd. Majid1Ahmad Izani Md. Ismail2Pusat Pengajian Sains Matematik, School of Mathematical Sciences, 11800 Pulau Pinang, MalaysiaPusat Pengajian Sains Matematik, School of Mathematical Sciences, 11800 Pulau Pinang, MalaysiaPusat Pengajian Sains Matematik, School of Mathematical Sciences, 11800 Pulau Pinang, MalaysiaNumerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.http://dx.doi.org/10.1155/2012/458701 |
| spellingShingle | Joan Goh Ahmad Abd. Majid Ahmad Izani Md. Ismail Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations Journal of Applied Mathematics |
| title | Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations |
| title_full | Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations |
| title_fullStr | Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations |
| title_full_unstemmed | Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations |
| title_short | Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations |
| title_sort | cubic b spline collocation method for one dimensional heat and advection diffusion equations |
| url | http://dx.doi.org/10.1155/2012/458701 |
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