Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients

Two implicit finite difference schemes for solving the two-dimensional multi-term time-fractional diffusion equation with variable coefficients are considered in this paper. The orders of Riemann–Liouville fractional time derivatives acting on spatial can be different various directions. By integrating original partial differential first, and second-order approximated by central quotients, then fully discrete scheme obtained after right rectangular quadrature formulae used to approximate resulting integrals. convergence analysis is given energy method, showing that first-order accurate second order space. Based a approximation using weighted shifted Grünwald operator, we present Crank–Nicolson prove it both Numerical results provided verify accuracy efficiency two proposed algorithms. theoretical generalized three-dimensional problems.