An Efficient Cubic B-Spline Technique for Solving the Time Fractional Coupled Viscous Burgers Equation

Abstract

The second order Burger’s equation model is used to study the turbulent fluids, suspensions, shock waves, and the propagation of shallow water waves. In the present research, we investigate a numerical solution to the time fractional coupled-Burgers equation (TFCBE) using Crank–Nicolson and the cubic B-spline (CBS) approaches. The time derivative is addressed using Caputo’s formula, while the CBS technique with the help of a θ-weighted scheme is utilized to discretize the first- and second-order spatial derivatives. The quasi-linearization technique is used to linearize the non-linear terms. The suggested scheme demonstrates unconditionally stable. Some numerical tests are utilized to evaluate the accuracy and feasibility of the current technique.

Keywords

• cubic B-spline
• coupled Burgers equation
• Crank–Nicolson finite difference technique
• Caputo derivative
• quasi-linearization