On the Limit Case of the Step-Reduction Method for Calculating Non Uniform Beam with Various Sections

In this paper, the step reduction method is discussed, which was advanced by Prof, Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.