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
