Development of Hybrid Block Integrator for the Numerical solution of Stiff and Oscillatory Differential Equations for first order Ordinary Differential Equations

Abstract

This paper discussed the development of a new numerical hybrid block integrator for the numerical solution of stiff and oscillatory differential equations for first order ordinary differential equations. The method of interpolation and collocation at some selected grid point to generate the continuous scheme was adopted. The research also investigates the consistency, convergence, zero-stability and region of absolute stability of the integrator using matlab and the integrator was tested on some numerical experiments for comparism. The analysis of the method showed that the method is Zero-stable, consistent, convergent and computationally stable. The method handles stiff and Oscillatory differential equations effectively. AMS Subject Classification: 65L05, 65L06, 65D3