(untitled) (Journal of Computational Mathematics, 2022)
A combined scheme of the improved two-grid technique with the block-centered finite difference method is constructed and analyzed to solve the nonlinear time-fractional parabolic equation. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and two linear problems based on the coarse-grid solutions and one Newton iteration is considered on a fine grid of size h. We provide the rigorous error estimate, which demonstrates that our scheme converges with order O(Δ t^2-α+h^2+H^4) on non-uniform rectangular grid. This result indicates that the improved two-grid method can obtain asymptotically optimal approximation as long as the mesh sizes satisfy h=O(H^2). Finally, numerical tests confirm the theoretical results of the presented method.