A novel approach for numerical analysis of ordinary differential equations (ODEs) is shown to cause an arbitrary initial function to conform to the solutions of sample ODEs.   By way of examples, the method is shown to consistently converge upon the solutions of initial value problems for two different step sizes. Further study is needed to determine if the method is stable for increasing smaller step sizes. Some advantages of this method are its simplicity, new approach to solving problems, and its potential to be applicable to a wide range of ODEs and partial differential equations that are useful in STEM fields.