A computational approach for solving time fractional differential equation via spline functions

https://doi.org/10.1016/j.aej.2020.06.007Get rights and content
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Abstract

A computational approach based on finite difference scheme and a redefined extended B-spline functions is presented to study the approximate solution of time fractional advection diffusion equation. The Caputo time-fractional derivative and redefined extended B-spline functions have been used for the time and spatial discretization, respectively. The numerical scheme is shown to be O(h2+Δt2-α) accurate and unconditionally stable. The proposed method is tested through some numerical experiments involving homogeneous/non-homogeneous boundary conditions which concluded that it is more accurate than existing methods. The simulation results show superior agreement with the exact solution as compared to existing methods.

Keywords

Redefined extended cubic B-spline functions
Caputo’s time fractional derivative
Advection–diffusion equation
Stability and convergence
Finite difference formulation

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Peer review under responsibility of Faculty of Engineering, Alexandria University.