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We propose a new method for the numerical solution of a class of twodimensional parabolic problems. Our algorithm is based on the use of the Alternating Direction Implicit (ADI) approach in conjunction with the Chebyshev tau meshless method based on the highest derivative (CTMMHD). CTMMHD is applied to solve the set of one-dimensional problems resulting from operator-splitting at each time-stage. CTMMHD-ADI yields spectral accuracy in space and second order in time. Several numerical experiments are implemented to verify the efficiency of our method.

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