## Abstract and Applied Analysis

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

#### 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 ${L}_{\infty }$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 849682, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277009

Digital Object Identifier
doi:10.1155/2014/849682

Mathematical Reviews number (MathSciNet)
MR3214457

Zentralblatt MATH identifier
07023192

#### Citation

Abbas, Muhammad; Majid, Ahmad Abd.; Ismail, Ahmad Izani Md.; Rashid, Abdur. Numerical Method Using Cubic Trigonometric B-Spline Technique for Nonclassical Diffusion Problems. Abstr. Appl. Anal. 2014 (2014), Article ID 849682, 11 pages. doi:10.1155/2014/849682. https://projecteuclid.org/euclid.aaa/1412277009

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