Numerical Method Using Cubic Trigonometric B-Spline Technique for Nonclassical Diffusion Problems. (20th May 2014)

• Record Type: Journal Article
• Authors: Abbas, Muhammad; Majid, Ahmad Abd.; Ismail, Ahmad Izani Md.; Rashid, Abdur
• Other Names: Zheng Sining Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-05-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/849682
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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 L 2 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.