Two-step Laguerre polynomial hybrid block method for stiff and oscillatory first-order ordinary differential equations

Abstract

We develop a two-step hybrid block method for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using the Laguerre polynomial as our basis function via interpolation and collocation techniques. The paper further investigates the basic properties of the method and found it to be zero-stable, consistent and convergent. The method was also tested on some sampled stiff and oscillatory problems and found to perform better than some existing ones with which we compared our results.