Solving Ordinary Differential Equations of First and Second Order Using a Single Numerical Algorithm with Four Equidistant Points

This paper investigates a distinct numerical algorithm for the solution of first and second orders initial value problems. The new method was developed using interpolation and collocation approach, with power series approximate solution used as interpolating polynomials. The numerical integrators of the block were obtained by evaluating the non-interpolation points within the chosen integration interval. To assess the efficiency of the proposed block method, it was tested on some first and second orders ordinary differential equations with initial value problems, and the results produced outperformed existing methods in terms of accuracy.