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The aim of this paper is to establish the convergence and error bounds to thefully discrete solution for a class of nonlinear systems of reaction-diffusionnonlocal type with moving boundaries, using a linearizedCrank-Nicolson-Galerkin finite element method with polynomial approximations ofany degree. A coordinate transformation which fixes the boundaries is used.Some numerical tests to compare our Matlab code with some existing movingfinite elements methods are investigated.

Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries