Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions

Abstract

This paper is concerned with the numerical approximation of the time fractional Burgers equation with nonsmooth solutions. A nonlinear fully discrete scheme is presented based on the nonuniform Alikhanov formula of the Caputo time fractional derivative and Fourier spectral approximation in space. The solvability of the scheme is proved by the fixed point theorem and a priori estimate. Using the error estimation method, the proposed scheme is stable and convergent with order O(τmin⁡{γσ,2}+N1−m), where τ,N,γ,m and σ are the maximum time step size, polynomial degree, grading parameter, spatial regularity and temporal regularity parameter of the exact solution, respectively. A numerical example is performed to support the theoretical results.