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Abstract: In this paper, an implicit one-step method for numerical solution of second order Initial Value Problems of Ordinary Differential Equations has been developed by collocation and interpolation technique. The one-step method was developed using Chebyshev polynomial as basis function and, the method was augmented by the introduction of offstep points in order to bring about zero stability and upgrade the order of consistency of the new method. An advantage of the derived continuous scheme is that it can produce several outputs of solution at the off-grid points without requiring additional interpolation. Numerical examples are presented to portray the applicability and the efficiency of the method.

Chebyshev Collocation Approach for a Continuous Formulation of Implicit Hybrid Methods for Vips In Second Order Odes