A simple numerical algorithm is derived for the time response to a time-invariant system, which is governed by a high order linear differential equation with constant coefficients. The technique involves determination of the partial-fraction expansion of rational functions. Only synthetic division and longhand division are required, so that it makes the process very suitable for computer programming. Meanwhile, due to the solution directly related to the system's initial conditions, the proposed approach requires only to compute the inversion of the generalized Vandermonde matrix.
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