An algorithm to evaluate the time response of a linear biological system from its transfer function

Abstract

The method described was developed to provide a numerical solution of the time response of a linear biological system from its transfer function. One advantage of the method is that the time response is expressed in the form of a transcendental equation, unlike previous solutions of this type which gave the time response as a sum of power series. A characteristic equation with a large number of roots can be solved, the accuracy of the time solution being determined by the accuracy with which the roots can be obtained and by that of the matrix inversion technique employed. The method has been found to give an accurate solution for roots differing by only 1.6666 × 10 −3 % so that even nearly equal roots can be accommodated.