The application of control theory to the numerical solution of ordinary differential equations

There exist many methods for the numerical solution of Ordinary Differential Equations. Euler, Taylor and Runge-Kutta are examples of one-step methods. Adams-Bashforth and Adams-Moulton are examples of multi-step methods. All methods approach the solution of the differential equation at different rates and their associated error, or distance from the solution, is of different order. We desire to apply control theory concepts, such as feedback, in order to minimize the error of the numerical solution.