Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations

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: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/458701
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spelling doaj-c249b04a417049779744bd48e746b99a2020-11-24T23:27:56ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Joan Goh
Ahmad Abd. Majid
Ahmad Izani Md. Ismail
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
author_facet Joan Goh
Ahmad Abd. Majid
Ahmad Izani Md. Ismail
author_sort Joan Goh
title 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_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_sort cubic b-spline collocation method for one-dimensional heat and advection-diffusion equations
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/458701
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AT ahmadabdmajid cubicbsplinecollocationmethodforonedimensionalheatandadvectiondiffusionequations
AT ahmadizanimdismail cubicbsplinecollocationmethodforonedimensionalheatandadvectiondiffusionequations
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