Abstract

In this research, we have proposed the numerical application of second derivative ordinary differential equations using power series for the direct solution of higher order initial value problems. The method was derived using power series, via interpolation and collocation procedure. The analysis of the method was studied, and it was found to be consistent, zero-stable and convergent. The derived method was able to solve highly stiff problems without converting to the equivalents system of first order ODEs. The generated results showed that the derived methods are notable better than those methods in literature. We further sketched the solution graph of our method and it is evident that the new method convergence toward the exact solution.