A Two-Grid Block-Centered Finite Difference Method for the Nonlinear Time-Fractional Parabolic Equation

In this article, a two-grid block-centered finite difference scheme is introduced 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 a linear problem is solved on a fine grid of size h. Stability results are proven rigorously. Error estimates are established on non-uniform rectangular grid which show that the discrete $$L^{\infty }(L^2)$$L∞(L2) and $$L^2(H^1)$$L2(H1) errors are $$O(\triangle t^{2-\alpha }+h^2+H^3)$$O(▵t2-α+h2+H3). Finally, some numerical experiments are presented to show the efficiency of the two-grid method and verify that the convergence rates are in agreement with the theoretical analysis.

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