Abstract:
This paper focuses on the development of three-step implicit numerical method capable of
solving second order Initial Value Problems of Ordinary Differential Equations. The collocation and
interpolation techniques are used in the derivation of the scheme and the Chebyshev polynomial is employed as
basis function. The scheme is applied as simultaneous integrator to second order initial value problem of ODEs.
The self-starting method developed which is capable of producing several outputs of solution at the off-grid
points without requiring additional interpolation, was implemented as block method so as to obtain solutions at
both step and offstep points. Numerical examples are presented to portray the applicability and the efficiency of
the method.
