A linear finite difference scheme for generalized time fractional Burgers equation

• A linear finite difference scheme is proposed to solve the generalized time fractional Burgers equation.
• The finite difference method is proved to be globally stable and convergent.
• The computational cost of the proposed method compares favorably to the usual implicit numerical schemes.

This paper is concerned with the numerical solutions of the generalized time fractional burgers equation. We propose a linear implicit finite difference scheme for solving the equation. Iterative methods become dispensable. As a result, the computational cost can be significantly reduced compare to the usual implicit finite difference schemes. Meanwhile, the finite difference method is proved to be unconditional globally stable and convergent. Numerical examples are shown to demonstrate the accuracy and stability of the method.