Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements

Authors

  • R. A. Adetona University of KwaZulu-Natal, School of Mathematics Statistics and Computer Science, Private Bag, X54001, Durban 4000, South Africa https://orcid.org/0000-0001-9167-7401
  • N. Parumasur University of KwaZulu-Natal, School of Mathematics Statistics and Computer Science, Private Bag, X54001, Durban 4000, South Africa https://orcid.org/0000-0003-1486-6203
  • P. Singh University of KwaZulu-Natal, School of Mathematics Statistics and Computer Science, Private Bag, X54001, Durban 4000, South Africa https://orcid.org/0000-0003-1941-7386

DOI:

https://doi.org/10.37256/cm.5220243900

Keywords:

B-Splines, space fractional diffusion equation, orthogonal collocation, finite elements

Abstract

In this paper, we consider the solution of the space fractional diffusion equation using orthogonal collocation on finite elements (OCFE) with quadratic B-spline basis functions. The main advantage of quadratic B-splines is that they have good interpolating properties and can be easily adapted for solving problems on non-uniform grids. The method is unconditionally stable and its convergence is also discussed. It is of order (3 − α) for 1 < α < 2. We present various linear and nonlinear examples. The solutions compared favourably with previous results in the literature.

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Published

2024-04-02

Issue

Contemporary Mathematics, Volume 5 Issue 2 (2024), 1122-2592

Section

Research Article

License

Copyright (c) 2024 R. A. Adetona, N. Parumasur, P. Singh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Solution of the Space Fractional Diffusion Equation Using Quadratic B-Splines and Collocation on Finite Elements. Contemp. Math. [Internet]. 2024 Apr. 2 [cited 2025 Dec. 24];5(2):1775-99. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/3900