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

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摘要 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.
出处 《Journal of Computational Mathematics》 SCIE CSCD 2022年第3期453-471,共19页 计算数学(英文)
基金 supported by the National Natural Science Foundation of China(Grant 11901489) China Postdoctoral Science Foundation(Grants BX20190187,2019M650152) supported by the State Key Program of National Natural Science Foundation of China(Grant 11931003) National Natural Science Foundation of China(Grants 41974133,11671157) supported by the Shandong Province Natural Science Foundation(Grant ZR2018MAQ008) National Natural Science Foundation of China(Grant 11771375).
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