Second-order nonuniform time-stepping schemes for time-fractional evolution equations with general elliptic operator

Abstract

We extend the numerical methods in Lyu and Vong (2021) to the time-fractional evolution equations with general elliptic operator. By reformulating the mixed derivatives part of the elliptic operator and introducing a different auxiliary multiplicative function, the Alikhanov type schemes are proposed for the governing problems on general time meshes. Unconditional stability and second-order convergence are obtained by energy method.