A modified numerov integration method for second order periodic initial-value problems

Abstract
A two-step P-stable method for the numerical integration of periodic initial value problems is derived. By the analysis of the error term a good estimate for the present period can be made. It is shown that the obtained implicit method can be made explicit by use of an analogous lower order method. In both cases a stability analysis is given. The superiority of these methods over other available methods is illustrated by two examples.