Bernstein polynomial induced two step hybrid numerical scheme for solution of second order initial value problems
Keywords:Bernstein polynomial,, Hybrid Block method, Collocation, Interpolation, Zero Stability, Consistency, Region of Absolute stability
This paper presents a two-step hybrid numerical scheme with one off-grid point for the numerical solution of general second-order initial value problems without reducing to two systems of the first order. The scheme is developed using the collocation and interpolation technique invoked on Bernstein polynomial. The proposed scheme is consistent, zero stable, and is of order four($4$). The developed scheme can estimate the approximate solutions at both steps and off-step points simultaneously using variable step size. Numerical results obtained in this paper show the efficiency of the proposed scheme over some existing methods of the same and higher orders.
How to Cite
Copyright (c) 2021 Journal of Mathematical Analysis and Modeling
This work is licensed under a Creative Commons Attribution 4.0 International License.