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

• Main Authors: Nauman Khalid, Muhammad Abbas, Muhammad Kashif Iqbal, Jagdev Singh, Ahmad Izani Md. Ismail
• Format: Article
• Language: English
• Published: Elsevier 2020-10-01
• Series: Alexandria Engineering Journal
• Subjects: Redefined extended cubic B-spline functions; Caputo’s time fractional derivative; Advection–diffusion equation; Stability and convergence; Finite difference formulation
• Online Access: http://www.sciencedirect.com/science/article/pii/S111001682030257X

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.