Open Access
2014 Numerical Method Using Cubic Trigonometric B-Spline Technique for Nonclassical Diffusion Problems
Muhammad Abbas, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Abdur Rashid
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/849682


A new two-time level implicit technique based on cubic trigonometric B-spline is proposed for the approximate solution of a nonclassical diffusion problem with nonlocal boundary constraints. The standard finite difference approach is applied to discretize the time derivative while cubic trigonometric B-spline is utilized as an interpolating function in the space dimension. The technique is shown to be unconditionally stable using the von Neumann method. Several numerical examples are discussed to exhibit the feasibility and capability of the technique. The L2 and L error norms are also computed at different times for different space size steps to assess the performance of the proposed technique. The technique requires smaller computational time than several other methods and the numerical results are found to be in good agreement with known solutions and with existing schemes in the literature.


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Muhammad Abbas. Ahmad Abd. Majid. Ahmad Izani Md. Ismail. Abdur Rashid. "Numerical Method Using Cubic Trigonometric B-Spline Technique for Nonclassical Diffusion Problems." Abstr. Appl. Anal. 2014 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023192
MathSciNet: MR3214457
Digital Object Identifier: 10.1155/2014/849682

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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