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A new method for finite-difference analysis of high-speed interconnects with frequency-dependent parameters is presented. A set of differential equations are derived based on the equivalent circuit models of dispersive transmission lines. The finite-difference time-domain (FDTD) method is then employed to solve them involving no convolution computations. The proposed method has the identical memory requirement and computational expense as the recursive-convolution-based algorithm, while more accurate results are obtained. The generalized two-port equivalent model of transmission lines contributes to the convenience of dealing with arbitrary termination networks. In addition, a higher order (2,4) FDTD scheme is employed to improve the accuracy and efficiency of this algorithm. The validity and accuracy of the proposed method are illustrated by several numerical examples.