Order six block integrator for the solution of first-order ordinary differential equations

In this research work, we present the derivation and implementation of an order six block integrator for the solution of first-order ordinary differential equations using interpolation and collocation procedures. The approximate solution used in this work is a combination of power series and exponential function. We further investigate the properties of the block integrator and found it to be zero-stable, consistent and convergent. The block integrator is further tested on some real-life numerical problems and found to be computationally reliable.