Abstract:
The aim of this study is to develop a class of continuous hybrid numerical
methods for direct solution of general second-order initial value problem
of ordinary differential equations. The approach adopted in this work is by
interpolation and collocation of a basis function and its corresponding
differential system respectively. Interpolation of the basis function was
done at both grid and off-grid points while the differential systems are
collocated at all grid points for different step-number k. This is to ensure
that the hybrid points are at the y function . Substitution of the unknown
parameters into the basis function and simplification of the resulting
equation produced the required continuous, consistent and symmetric
hybrid methods. Attempts were made to derive predictors of the same
order with the methods to circumvent the inherent disadvantage of
predictor methods of lower order. The methods were applied to solve linear
and nonlinear second-order initial value problems directly. Errors in the
results obtained were compared with those of the existing methods of the
same and even of higher order. The comparison shows that the accuracy
of the new methods is better than the existing methods.
