Convergence and stability of the finite difference scheme for nonlinear parabolic systems with time delay*

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In this article, a class of nonlinear evolution equations – reaction–diffusion equations with time delay – is studied. By combining the domain decomposition technique and the finite difference method, the results for the existence, convergence and the stability of the numerical solution are obtained in the case of subdomain overlap and when the time-space is completely discretized.

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