A Multistep Method for a Special Class of Second—Order Differential Equations

Abstract

A multi–step numerical method for the solution of second order ordinary differential equation was developed by interpolating in a finite range with a basis function. The basis function consists of a combination of exponential and trigonometric functions to ensure that such problems possess unique and continuously differentiable solutions. The method has been tested and found to be reliable, efficient and less tedious than other multi-step methods which require reduction of higher order equations into several first order equations. The method was applied to some special second order equations arising from mechanics and engineering problems. The requisite numerical properties were obtained.