Abstract
A fully discrete two-grid modified method of characteristics (MMOC) scheme is proposed for nonlinear variable-order time-fractional advection–diffusion equations in two space dimensions. The MMOC is used to handle the advection-dominated transport and the two-grid method is designed for efficiently solving the resulting nonlinear system. Optimal L2 error estimates are derived for both the MMOC scheme and the corresponding two-grid MMOC scheme. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed method.
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