A Combination of Power and Exponential Series for the Development of Hybrid Block Integrators for the Solution of First Order Ordinary Differential Equations

Abstract

The research article, presented the derivation and implementation of some block integrators at step sizes  and  respectively for the solution of first order ordinary differential equation via power and exponential series as basic functions. The derived methods were found to be zero-stable, consistent and convergent. Also for the values of  present in the basis were tested with various numbers within the number system, the schemes obtained remain the same. The newly derived methods displayed their superiority when tested on some real life problems and some non-linear differential equations.