Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique

Mohammad Tamsir; Neeraj Dhiman; Deependra Nigam; Anand Chauhan; Mohammad Tamsir; Neeraj Dhiman; Deependra Nigam; Anand Chauhan

doi:10.3934/math.2021226

AIMS Mathematics

2021, Volume 6, Issue 4: 3805-3820. doi: 10.3934/math.2021226

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Research article

Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique

1.
Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia
2.
Department of Mathematics, Graphic Era Hill University, Dehradun, India
3.
Department of Mathematics, Graphic Era University, Dehradun, India
4.
D. A. V. (P. G.) College, Dehradun, India

Received: 04 November 2020 Accepted: 10 January 2021 Published: 28 January 2021
MSC : 35XX, 65N12

The purpose of this work is to find the numerical solution of the Caputo time-fractional diffusion equation using the modified cubic exponential B-spline (CExpB-spline) collocation technique. First, the CExpB-spline functions are modified and then used to discretize the space derivatives. Three numerical examples are considered for checking the efficiency and accuracy of the method. The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. Von Neumann stability is carried out which gives the guarantee that the technique is unconditionally stable. The rate of convergence is also obtained. Furthermore, this technique is efficient and requires less storage.
- Caputo time-fractional diffusion equation,
- collocation technique,
- CExpB-spline functions,
- stability analysis
Citation: Mohammad Tamsir, Neeraj Dhiman, Deependra Nigam, Anand Chauhan. Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique[J]. AIMS Mathematics, 2021, 6(4): 3805-3820. doi: 10.3934/math.2021226

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Abstract

The purpose of this work is to find the numerical solution of the Caputo time-fractional diffusion equation using the modified cubic exponential B-spline (CExpB-spline) collocation technique. First, the CExpB-spline functions are modified and then used to discretize the space derivatives. Three numerical examples are considered for checking the efficiency and accuracy of the method. The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. Von Neumann stability is carried out which gives the guarantee that the technique is unconditionally stable. The rate of convergence is also obtained. Furthermore, this technique is efficient and requires less storage.

References

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