Enhanced Numerov Method for the Numerical Solution of Second Order Initial Value Problems

Abstract

Numerov method is a multistep numerical method that is used in solving second order differential equations. In this work, we apply this method as a Boundary Value Method (BVM) for the numerical approximation of both linear and nonlinear second order initial value problems. This is achieved by constructing the Numerov method via interpolation and collocation process while utilizing data at off-step points and implementing it as a BVM. On comparing the results obtained from the solved problems, it shows that the method is accurate with high level of convergence to their exact forms and performs better than results from literature.