Abstract:
This thesis focuses on the derivation, analysis and implementation of one-step, two-step, three-step
and four-step Continuous Hybrid-Block Methods with Legendre polynomial as basis function for
direct solution of second order initial value problems of ordinary di erential equation. The approach
is based on Collocation of the equation arising from the basis function and the di erential equation at
both the grid and o -grid points and interpolation of the approximate solution at the selected points.
To estimate the order of the schemes, Taylor series expansion was adopted. The derived schemes were
implemented in block mode and then applied on some second order initial value problems of ordinary
di erential equations, the results showed that the methods converge as step-size(h) decreases. The
methods were shown to be Consistent and Zero stable, hence Convergent. Accuracy comparison
was also made with the existing methods and it was found out that the derived schemes compared
favourably with existing ones.
