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

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