Fully Implicit Hybrid Block –Predictor Corrector Method for the Numerical Integration of y″' = f(x, y, y', y''), y(xο)= ηο, y'(xο) = η1, y''(xο) = η3

A fully implicit hybrid Block- Predictor Corrector method for the numerical integration of initial value problems of third order ordinary differential equations is presented in this paper. We adopted the approach of collocation approximation in the derivation of the scheme to generate a scheme with continuous coefficients, from where additional schemes were developed. The implementation strategy involves combination of the main scheme and other additional schemes as simultaneous Integrator to initial value problems of third order ordinary differential equations. Properties analysis of the block method showed that it is consistent, convergent, zero stable and absolutely stable. Numerical examples were given.