Three-Step Implicit Block Method for Second Order Odes

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.