NUMERICAL INTEGRATOR FOR THE SOLUTION OF TWO HYBRID POINTS FOR STIFF AND OSCILLATORY DIFFERENTIAL EQUATIONS FOR FIRST ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This research paper examined the implementation of a hybrid integrator for the solution of Stiff and Oscillatory first order initial value problems of Ordinary Differential Equations. The hybrid integrator was derived by collocation and interpolation of the combination of power series and exponential function at some selected grid and off-grid points to generate a linear multistep method which is implemented in block form. The paper further investigated the properties of the block integrator and found it to be zero-stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some notable numerical examples and the results was found to compete favourably with some existing methods.