A CLASS OF HYBRID METHODS FOR THE SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS

Abstract

This work is based on the derivation of a class of hybrid methods for the solution of rst order initial value problems (IVPs) in block method. The research makes use of Power series as the basis function. This is achieved by the technique of collocation and interpolation of equations arising from the combination of the di erential system and the basis function. Continuous linear multi-step method of step number k = 2; and 3 were developed by interpolating the basis function at some certain grid points and collocating the di erential system at both grid and o -grid points which gives a class of hybrid methods. The unknown parameters in the system of linear equation arising from the collocation and interpolation functions were determined. The values were substituted in the approximate solution to generate a class of hybrid methods which are simultaneously applied as numerical integration by assembling them into block methods. Analysis of the methods were carried out based on order, zero stability, consistency and convergence. Boundary locus method was adopted to obtain the region of absolute stability of the methods. Six numerical illustrations were presented in order to determine the level of accuracy of the new methods and the results obtained yielded better accuracy when compared with some existing methods