An Ideal Symmetric Predictor-Corrector Approach for Solving Second-Order Ordinary Differential Equations

Abstract

The second order initial value problems are generally integrated numerically by development of
numerical methods designed specifically for second order differential equations. In this work, a
symmetric corrector method is presented capable to integrate real-life problems modeled into
second order ordinary differential equations directly. The power series is used as a basis function
which was interpolated and collocation was done at its second derivative of only grid points.
This is to ensure that the hybrid points are at they function  . The resulting systems of
equations is solved and after necessary simplifications continuous method is obtained. Attempts
were also made to develop predictors of the same order with the method to circumvent the
inherent demerit of predictor methods. The method is of optimal order, symmetric, consistent,
and zero-stable. The discrete method obtained is applied to solve real-life problems with better
performance.