Numerical solutions of advection diffusion equations involving Atangana–Baleanu time fractional derivative via cubic B-spline approximations

Abstract

The B-spline or the basis spline function, is a piecewise polynomial function made up of polynomials, its domain is subdivided by knots, and basis functions are non-zero on the entire domain. In this study, a new cubic B-spline (NCBS) approximation together with the θ-weighted scheme is formed to approximate the numerical solution of the time fractional advection diffusion equation (TFADE) involving the Atangana–Baleanu time fractional derivative (ABTFD). The finite difference scheme (FDS) is utilized to discretize the ABTFD with a non-singular kernel. The spatial derivative is discretized by using NCBS functions. The stability analysis of the proposed technique is studied. Convergence analysis of the current technique is also analyzed. The proposed technique is examined on a variety of problems, and the numerical outcomes are contrasted with the previously published technique’s results to ensure the correctness and accuracy of the current technique.

Keywords

• New approximation
• Cubic B-spline functions
• Time fractional advection diffusion equation
• Atangana–Baleanu time fractional derivative
• Stability
• Convergence