HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

摘要

This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation.First,we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives.Second,based on the piecewise-quadratic polynomials,we construct the nodal basis functions,and then discretize the multi-term fractional equation by the finite volume method.For the time-fractional derivative,the finite difference method is used.Finally,the iterative scheme is proved to be unconditionally stable and convergent with the accuracy O(σ^(2)+τ^(2-β)+h^(3)),whereτand h are the time step size and the space step size,respectively.A numerical example is presented to verify the effectiveness of the proposed method.