A two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations
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Date
2022-12-31
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Abstract
A continuous two-step block method with two hybrid points for the numerical solution of first
order ordinary differential equations is proposed. The approximate solution in form of power series and
its first ordered derivative are respectively interpolated at the point x = 0 and collocated at equally spaced
points in the interval of consideration. The application of the method involves using the main scheme derived
together with the additional schemes simultaneously to obtain the solution to the problem at the grid points.
The analysis of the method and the results obtained from the examples considered show that the method is
consistent, zero-stable, convergent and of high accuracy.