Linear differential equation with constant coefficients solved by matrix formulation
By the formulation of matrix function, a system of linear differential equations with constant coefficients can be uniquely solved. The desired solution is simply expressed as the matrix product of two factors: (1) a variable vector, uniquely derived from the given system, can be set aside after it is found; and (2) a constant matrix, directly related to the initial conditions, is computed numerically. The effort of re-computation is very minimal upon the initial conditions changed. For the classical Laplace transformation, the solution of the differential equation must be recalculated from the very beginning whenever the initial conditions are altered. A typical numerical example is provided in detail to show the merit of the approaches presented.
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