Numerov solution of linear second order ordinary differential equations containing first order derivative term

Abstract

A central activity in the numerical solution of differential equations is that of finding effective numerical methods to solve particular types of problems. One of such problems is the second order ordinary differential equations of the form ?′′=?(?,?). A very important algorithm towards the solution of this equation is the Numerov method. In this present work, the Numerov method is employed to solve linear second order ordinary differential equations involving a first derivative term. By a transformation of the equation, the first derivative term is eliminated by representing it with finite difference quotient at the grid points, resulting in an equation that makes it suitable for solution. Once this equation is solved, the approximate solution of the desired function ?(?) can be obtained at the grid points. Extensive numerical tests to illustrate the effectiveness and reliability of the method are presented. The numerical experiments were conducted using Maple 2019.0 software package.