Abstract:
This work is based on the derivation of four-step block hybrid methods for the solution of
second order initial value problems (IVPs) in block mode. Power series was used as the basis
function. Techniques of collocation and interpolation were used in the differential system
arising from the basis function and interpolating functions respectively. Continuous linear
multistep methods with step number k = 4 were developed by interpolating the basis function
at some certain grid points and collocating the differential system at both grid and off-grid
points. Unknown parameters in the system of linear equation arising from the collocation
and interpolation functions were determined. Consequently the values were substituted into
the approximate solution, to generate hybrid methods which were simultaneously applied
as numerical integrators by assembling them into block methods. Analysis of the methods
were carried out to determine consistency, order, zero stability,convergency, and region of
absolute stability. The new methods were tested on some differential equations to determine
their efficiency and accuracy, introduction of a hybrid point between points of interpolation
validates its superiority over some existing methods in terms of accuracy when solving the
considered numerical examples. Thus, numerical solutions obtained yield better results
when compared with some existing methods.
