AN IMPROVED TWO-GRID TECHNIQUE FOR THE NONLINEAR TIME-FRACTIONAL PARABOLIC EQUATION BASED ON THE BLOCK-CENTERED FINITE DIFFERENCE METHOD

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(∆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.