keywords: Collocation, continuous scheme, interpolation, Laguerre polynomial
In this paper, an implicit one-step method with three off-grid points for numerical solution of second order initial value problems of ordinary differential equation has been developed by collocation and interpolation technique. The one-step method was developed using Laguerre polynomial as basis function and the method was augmented by the introduction of off-step points in order to bring zero stability and upgrade the order of consistency of the 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 solved with the aid of MAPLE software package. We observed that the results obtained from the method converged faster when the numbers of off-step points were increased and this validate the consistency and zero stability of the method.
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