Abstract
The main purpose of this paper is to construct a semi-implicit difference scheme for the multi-term time-fractional Burgers-type equations. Firstly, the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives. Secondly, the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear convection term $$uu_x$$ is discretized via the semi-implicit method. Then, a fully discrete finite difference scheme is established. The unconditional stability and convergence in maximum-norm are derived by the discrete energy method and the mathematical induction. Numerical experiments are performed to validate the theoretical analysis.
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