A comparative analysis of Numerov and Nystrom methods

Abstract

In this paper, two test problems were used to study the behaviour and performance of two numerical methods (Numerov and Nystrom) of solving second order initial value problem (IVP) of ordinary differential equation without the first order term. A test implementation of each of the methods and a comparative analysis of the two methods was done. The result showed that only Nystrom method is suitable for solving problems with negative exponential solution as Numerov method provided no meaningful approximation to it. Also both Numerov and Nystrom methods provided
reasonable approximation for problems with cosine solution, but with Nystrom consistently providing a better approximation.