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In this article, a linear block-centred finite difference method for the nonlinear distributed-ordered diffusion differential equation with Neumann boundary condition is constructed and analysed. We derive rigorous error estimates and obtain the optimal order of convergenceboth for pressure and velocity, whereare the step sizes in time, distributed order and space, respectively. Finally, some numerical experiments are presented to show the efficiency and accuracy of our constructed scheme.

Error estimate of a finite difference method for the nonlinear distributed-ordered diffusion equation on staggered grids