Integration of First-order Modeled Differential Equations Using a Quarter-step Method

In this paper, we present the derivation and implementation of a quarter-step method for the integration of first-order modeled differential equations. The quarter-step method was developed using Laguerre polynomial of degree six as our basis function via interpolation and collocation techniques. We went further to apply the quarter-step method developed on some modeled first order differential equations. The paper also analyzed the basic properties of the method derived. From the results obtained, it is obvious that the method is computationally reliable.