A self-starting four-step fifth-order block integrator for stiff and oscillatory differential equations

Abstract

This paper examines the derivation and implementation of a self-starting four-step fifth order block integrator for direct integration of stiff and oscillatory first-order ordinary differential equations using interpolation and collocation procedures. The method was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit linear multistep method. The paper further investigates the properties of the block integrator and found it to be zero-stable, consistent and convergent. The efficiency of the integrator was also tested on some sampled stiff and oscillatory problems and found to perform better than some existing ones.