A Quarter-Step Hybrid Block Method for First-Order Ordinary Differential Equations

In this paper, we derive a new quarter-step hybrid block method for the solution of first-order Ordinary Differential Equations (ODEs). We employ the approach of interpolating the power series and collocating the differential system within a quarter-step interval of integration. The evaluation is carried out at off grid points within the step of the method to produce various discrete schemes to form our block method. The basic properties of the new hybrid block method were further investigated. The new method was also tested on some problems and the results obtained were found to compete favorably with those of the existing ones.