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Numerical Method Using Cubic Trigonometric B‐Spline Technique for Nonclassical Diffusion Problems

Author

Listed:
  • Muhammad Abbas
  • Ahmad Abd. Majid
  • Ahmad Izani Md. Ismail
  • Abdur Rashid

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 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.

Suggested Citation

  • Muhammad Abbas & Ahmad Abd. Majid & Ahmad Izani Md. Ismail & Abdur Rashid, 2014. "Numerical Method Using Cubic Trigonometric B‐Spline Technique for Nonclassical Diffusion Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:849682
    DOI: 10.1155/2014/849682
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    References listed on IDEAS

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    1. Joan Goh & Ahmad Abd. Majid & Ahmad Izani Md. Ismail, 2012. "Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-8, May.
    2. Yisheng Lai & Weiping Du & Renhong Wang, 2013. "The Viro Method for Construction of Piecewise Algebraic Hypersurfaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, September.
    3. Yisheng Lai & Weiping Du & Renhong Wang, 2013. "The Viro Method for Construction of Cr Piecewise Algebraic Hypersurfaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Joan Goh & Ahmad Abd. Majid & Ahmad Izani Md. Ismail, 2012. "Cubic B‐Spline Collocation Method for One‐Dimensional Heat and Advection‐Diffusion Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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