A combined scheme of the improved two-grid technique with the block-centered fi-nite 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(Δt2-a+h2+H4)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(H2).Finally,numerical tests confirm the theoretical results of the presented method.

Xiaoli Li;Yanping Chen;Chuanjun Chen

School of Mathematics,Shandong University,Jinan 250100,China;School of Mathematical Science,South China Normal University,Guangzhou 520631,China;School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China

计算数学（英文版）

[1]Xiaoli Li;Yanping Chen;Chuanjun Chen-.AN IMPROVED TWO-GRID TECHNIQUE FOR THE NONLINEAR TIME-FRACTIONAL PARABOLIC EQUATION BASED ON THE BLOCK-CENTERED FINITE DIFFERENCE METHOD)[J].计算数学（英文版）,2022(03):453-471

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