A Numerical Hybrid Block Integrator for Solving First Order Oscillatory and Exponential Differential Equations

In this paper, a numerical hybrid block method is designed for the solutions of oscillatory and exponential first-order initial value problems in ordinary differential equations (ODEs). In deriving the method, we used the method of Collocation and Interpolation of power series approximation to generate a one-tenth-step continuous Block scheme. The convergence properties along with the stability and Consistency of the method were shown. It was concluded that the developed method is convergent, consistent, and zero-stable. From the numerical computations of absolute errors carried out using the newly derived method, it was found that the method performed better than the method with which we compared our results.