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

2021 ◽  
Vol 6 (4) ◽  
pp. 3805-3820
Author(s):  
Mohammad Tamsir ◽  
◽  
Neeraj Dhiman ◽  
Deependra Nigam ◽  
Anand Chauhan ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Collocation ◽  
B Spline ◽  
Collocation Technique ◽  
Time Fractional Diffusion Equation

A modified trigonometric cubic B-spline collocation technique for solving the time-fractional diffusion equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Neeraj Dhiman ◽  
M.J. Huntul ◽  
Mohammad Tamsir
Keyword(s):  
Diffusion Equation ◽  
Numerical Technique ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Dirichlet Boundary Conditions ◽  
Unconditionally Stable ◽  
Content Type ◽  
B Spline ◽  
Time Fractional Diffusion Equation ◽  
The Stability

Purpose The purpose of this paper is to present a stable and efficient numerical technique based on modified trigonometric cubic B-spline functions for solving the time-fractional diffusion equation (TFDE). The TFDE has numerous applications to model many real objects and processes. Design/methodology/approach The time-fractional derivative is used in the Caputo sense. A modification is made in trigonometric cubic B-spline (TCB) functions for handling the Dirichlet boundary conditions. The modified TCB functions have been used to discretize the space derivatives. The stability of the technique is also discussed. Findings The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. The stability analysis shows that the method is unconditionally stable. Furthermore, this technique is efficient and requires less storage. Originality/value The current work is novel for solving TFDE. This technique is unconditionally stable and gives better results than existing results (Ford et al., 2011; Sayevand et al., 2016; Ghanbari and Atangana, 2020).

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