An optimization of the phase-plane-delta method for the solution of non-linear differential equations

An improvement to the phase-plane-data method of solving non-linear differential equations of the type ${d^2}x/d{t^2} + H\left ( x \right ) = 0$ is discussed. This improvement provides a means of determining an optimized value of the parameter $p$, frequency. In the conventional phase-plane-delta method the parameter $p$ is chosen either arbitrarily or as the coefficient of the positive linear term. The phase-plane trajectory and period of oscillation can be more readily determined by this method than by the conventional phase-plane-delta method.