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A fast simulation method for time-derivative cellular neural networks (TDCNN) is proposed. Using forward Euler approximation (FEA) for the derivative of the cell state and the backward Euler approximation (BEA) for the derivatives of the neighboring cell states enables the recursive computation of the cell state and provides a speed advantage of orders of magnitude. The state equations are then packed into a vector-matrix form which enables the previously empirically given time constraint to be expressed as a matrix condition. It is shown that using both FEA and BEA leads to a second-order difference equation whose corresponding second-order differential equation is derived and shown to yield the same simulation results.