A second-order BDF compact difference scheme for fractional-order Volterra equation

In this paper, a second-order backward differentiation formula compact difference scheme with the truncation error of order 1+α(0<α<1) for time and 4 for space to fractional-order Volterra equation is considered. The integral term is treated by means of the second-order convolution quadrature suggested by Lubich and fourth-order accuracy compact approximation is applied for the second-order space derivative. The stability and convergence of the compact difference scheme in a new norm are proved by the energy method. Numerical experiments that are in total agreement with our analysis are reported.